tag:blogger.com,1999:blog-25256434198765346482017-07-01T23:33:59.389-07:00Factor/factorization (trinomial, polynomial, binomcharukishnanihttp://www.blogger.com/profile/13610526395933622565noreply@blogger.comBlogger41125tag:blogger.com,1999:blog-2525643419876534648.post-25842081590979134122013-04-06T05:48:00.001-07:002013-04-06T05:48:04.910-07:00affordable wedding invitation card<p>
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<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Polynomials can be factored using either the synthetic division technique or mid – term splitting (in case of quadratic polynomials). If the quadratic polynomials are possible to be factored, their middle term is split and we get the roots. The other way is to use the formula directly to get two roots. Let us consider some examples to know how <a href="http://www.tutorcircle.com/factoring-polynomials-sqA4i.html"><strong>polynomial factoring</strong> </a>is done:</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Example 1: Factorize the polynomial 5 x<sup>2</sup> + 8 x + 3 = 0?</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Solution: The given polynomial is of degree two and so number of roots it would possess will be 2. As it is possible to split the middle term of this polynomial, we do it as follows:</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">5x<sup>2</sup> + 8 x + 3 = 0,</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Or 5 x<sup>2</sup> + 5 x + 3 x + 3 = 0,</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Or 5 x (x + 1) + 3 (x + 1) = 0,</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Or x = -1, -3 /5.</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Example 2: Suppose we need to find the highest common factor between x<sup>3</sup> + 2x<sup>2</sup> + 8 and x<sup>2</sup> + x + 4?</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Solution: In such a case we use the synthetic division technique as follows:</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">x<sup>3</sup> + 2 x<sup>2</sup> + 8 / x<sup>2</sup> + x + 4; Remainder = x<sup>2</sup> + 4,</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">x<sup>2</sup> + x + 4 / x<sup>2</sup> + 4; Remainder = x,</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">x<sup>2</sup> + 4 /x; Remainder = 4,</span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">We see 4 is the common factor between two polynomials x<sup>3</sup> + 2 x<sup>2</sup> + 8 and x<sup>2</sup> + x + 4.</span></span></span><br />
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<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">The <strong><a href="http://math.tutorvista.com/statistics/likelihood-ratio-test.html">likelihood ratio test</a></strong> is an approach to match probability of occurrence of a certain value under one theory against the probability of the same value under another theory. The 2nd one is the more limited theory. </span></span></span><br />
<span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">These concepts are very important from the perspective of preparing <a href="http://exams.edurite.com/iit-jee~b2EO.html">iit entrance exam</a>.</span></span></span><br />
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manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-41892822726814063172012-08-28T02:45:00.003-07:002012-08-30T04:15:51.817-07:00factor polynomials<div dir="ltr" style="text-align: left;" trbidi="on"><span style="line-height: 0.45cm;">In the previous post we have discussed about </span><span style="color: #222222; font-size: 12px; line-height: 16px;"> </span><span class="Apple-style-span" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 17px;"><a href="http://polynomial-trimonial-binomial.blogspot.in/2012/08/how-do-you-determine-if-polynomial-is_16.html" style="color: #5dc2c0; text-decoration: none;">How do you Determine if a Polynomial is the Difference of Two Squares</a> </span><span class="Apple-style-span" style="line-height: 17px;">and In today's session we are going to discuss about factor polynomials. We define polynomial as the expression which has the combination of different terms. If a polynomial has only one term, then we say that it is a linear polynomial. On the other hand, we say that the expression with two terms is a binomial and the expression with three terms is called a trinomial.</span><br />
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<div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">We can <strong><a href="http://www.tutorcircle.com/factoring-polynomials-sqA4i.html">factor polynomials</a></strong> and write them as the product of different expressions. There are different methods to find the factor of the given polynomials.</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">First method is by finding the common factors and taking them common. Suppose we have the polynomial say 4x>2 + 2x, so we find that 2x is common factor of both the terms in the given polynomial. So we will write the given polynomial as follows :</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">2x ( 2x + 1 ) .</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">Thus the given polynomial can be written as the product of 2x * ( 2x + 1 ).</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">Another method of finding the factors of the given polynomial is by breaking the middle term.</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">Let's us take the polynomial x>2 + 7x – 18:</div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; margin-bottom: 0cm; orphans: 2; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm; widows: 2;"><span class="Apple-style-span" style="line-height: 0.45cm;">We will break the middle term of the given polynomial such that the sum is 7x and the product is - 18x>2, which is the product of the first and the third term. </span><span class="Apple-style-span" style="line-height: 17px;">(know more about factor polynomials, <a href="http://en.wikipedia.org/wiki/Factorization_of_polynomials">here</a>)</span></div><div><br />
</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">Thus the given polynomial can be written as follows:</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">=2x>2 + 9x – 2x -18 ,</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">=2x>2 -2x + 9x -18,</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">= 2x (x – 1) + 9 (x – 1),</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">= (2x + 9) (x – 1) .</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">Some times the polynomial are similar to the standard identities, which can be directly written in their form.</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">For example if we have 9x>2 - 4y>2,</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">= (3x)>2 – (2y) >2 ,</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">=(3x – 2y ) (3x + 2y).</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">This solution is based on the identity a>2 – b>2 = ( a + b ) * ( a – b ) .</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><br />
</div><div style="border: none; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;">We can learn about <strong><a href="http://chemistry.tutorvista.com/biochemistry/protein-purification.html">Protein Purification</a></strong> online. <a href="http://boards.edurite.com/cbse+board-class+10-sample-question-paper~beN-cMB.html">cbse sample papers for class 10 </a>are also available online. </div></div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-92087320562449469682012-08-16T03:37:00.001-07:002012-08-16T03:37:14.510-07:00How do you Determine if a Polynomial is the Difference of Two Squares<p>
<span style="font-size: 10pt; line-height: 0.45cm; ">Hi friends, we will discuss <strong>How do you Determine if a Polynomial is the Difference of Two Squares</strong>. Polynomials are expressions in such a way that it consist of variables with exponents and constants values. Exponent values present in a polynomial expression is of any degree. Generally these Polynomials expression are used in Trigonometry, calculus, algebra and so on. There is a rule defined in polynomials so that polynomial contain constant, variables, exponents and operations but they cannot have any type of division operator in expression. Polynomial expression don’t have Radicals, infinite number or any type of negative exponent. Now now we will understand that How do you Determine if a Polynomial is the Difference of Two Squares.</span></p>
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<font color="#000000"><font face="Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati"><font size="2" style="font-size: 10pt">Now we will use some step to solve polynomial:<br />
<strong>Step 1:</strong> To find polynomial first we need to solve the given expression. For example: suppose that we have given a polynomial expression 2p<sup>2</sup> + 2p<sup>2</sup> - 10 – 6. Now we have to solve it as 4p<sup>2</sup> – 16.<br />
<strong>Step 2:</strong> Then test the Integer value present in equation. The integer value present in equation is a perfect Square. In the equation integer value is 16 that is a perfect square. If we want to write it in terms of exponent then we can also write. It can be written in exponent form as 4<sup>2</sup>.<br />
<strong>Step 3:</strong> Now we will see again the equation and also check that if it is make a difference of two perfect square number that this equation is denotes a subtraction of two perfect square terms. Now we have to set above equation in format of subtraction of two square terms that is p<sup>2</sup> – q<sup>2</sup>.<br />
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<strong>Step 4:</strong> Now we have to find the factor of this equation by using the difference of two square formula that is (p + q) (p - q). Then we get the equation 4p<sup>2</sup> – 16 that is written in factorized form as (2p + 4) (2p - 4).</font></font></font></p>
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<font color="#000000"><font face="Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati"><font size="2" style="font-size: 10pt"><strong>Standard Deviation of the Mean</strong> is a set of data are usually reported together. To prepare for iit then prefer online iit jee syllabus.</font></font></font></p>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-75881933405302292762012-08-14T00:23:00.002-07:002012-08-14T01:27:42.827-07:00How do you Determine if a Polynomial is the Difference of Two Squares<div dir="ltr" style="text-align: left;" trbidi="on">In the previous post we have discussed about <span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><a href="http://polynomial-trimonial-binomial.blogspot.in/2012/08/factoring-polynomials-calculator.html" style="color: #249fa3; text-decoration: none;">Factoring Polynomials Calculator</a> </span>and In today's session we are going to discuss about How do you Determine if a Polynomial is the Difference of Two Squares. Hi friends, in mathematics, we will see different methods to solve a polynomial expression. Before learning <strong><a href="http://www.tutorcircle.com/how-do-you-determine-if-a-polynomial-is-the-difference-of-two-squares-fCzOq.html">How do you Determine if a Polynomial is the Difference of Two Squares</a></strong>. First it is necessary to learn about definition of polynomial. Polynomial can be defined as any types of expression that can be written using constant, variable and exponent values in it. For example: 4ab<sup>2</sup> + 7xy<sup>2</sup> – 4x – 25. Given example is a polynomial expression. Now we will understand that How do you Determine if a Polynomial is the Difference of Two Squares. Steps to follow to determine polynomial differences are shown below: (know more about Polynomial, <a href="http://en.wikipedia.org/wiki/Polynomial">here</a>)<br />
<div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong>Step 1:</strong> The word difference means subtraction. It means subtract one value to other value. For example: The difference of 9 and 3 is given as 3, in mathematical it can be written as: 9 – 6 = 3.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong>Step 2:</strong> If we want to calculate if a polynomial is the difference we need to subtract one polynomial value other polynomial value.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong>Step 3:</strong> Then we have to check the answer that it matches a given polynomial or not.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong>Step 4:</strong> To satisfy the above statement, the given polynomial can be ready to be factorized into two different factors. For example we have an polynomial expression: p<sup>2</sup> – q<sup>2</sup>. As we see this, it is an difference of polynomial two squares. If we find the factor of given example then it can be written as:</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">= p<sup>2</sup> – q<sup>2</sup>, on finding it factor we get:</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">= (p + q) (p – q), here we get the difference of two squares.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">In this square polynomial case power value of square should be even, if power of polynomial expression are odd then it is not square polynomial. In this way we can easily solve the square polynomial expression.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong><a href="http://chemistry.tutorvista.com/physical-chemistry/quantum-theory.html">Quantum Field Theory</a></strong> can be defined as a basic mathematical language which is used to express</span></span></span> and analyze the physics of elementary particles. It is an important topic for <a href="http://exams.edurite.com/iit-jee-syllabus~b2EO.html">iit jee syllabus</a>.</div><div style="border: none; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><br />
</div></div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-18235275664354058902012-08-08T23:34:00.002-07:002012-08-09T02:12:09.662-07:00Factoring Polynomials Calculator<div dir="ltr" style="text-align: left;" trbidi="on"><span style="font-size: 10pt; line-height: 0.45cm;">In the previous post we have discussed about </span><span class="Apple-style-span" style="font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 13px; line-height: 17px;"><a href="http://polynomial-trimonial-binomial.blogspot.in/2012/08/polynomial-factoring-calculator.html" style="color: #249fa3; text-decoration: none;">polynomial factoring calculator</a> </span><span style="font-size: 10pt; line-height: 0.45cm;">and In today's session we are going to discuss about Factoring Polynomials Calculator. Hello friends, in this blog we will understand that how to <strong><a href="http://www.tutorcircle.com/factoring-polynomials-calculator-ca4S9lc.html">Factoring Polynomials Calculator</a></strong>. If in any equation constant value, variables and exponent values are present then it is polynomial expression. For example: 3xy</span><sup style="line-height: 0.45cm;">2</sup><span style="font-size: 10pt; line-height: 0.45cm;"> – 6x + 2y</span><sup style="line-height: 0.45cm;">3</sup><span style="font-size: 10pt; line-height: 0.45cm;">– 20. As we see in given expression that polynomial expression is joined with mathematical operators. In mathematics, Negative and fraction values are also present in case of polynomial expression. It never joined by division operator.</span><br />
<br />
<div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Polynomial factoring calculator is a type of machine that help us to calculate tough problem very easily. Let’s discuss some steps to calculate the factor of polynomial expression.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong>Step 1:</strong> Put polynomial expression in first text box.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong>Step 2:</strong> Or enter coefficient of square, cube in one text box and coefficient of ‘x’ in next text box and constant in last text box.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong>Step 3:</strong> Then press solve button to get result.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">By using the given steps we can calculate the factor of polynomial expression.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Now we will discuss how to find factor of polynomials expression. Here we will discuss quadratic method to find polynomial expressions.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Let’s have a polynomial expression u<sup>2</sup>+ 4u – 10, we can factorize this polynomial as shown below:</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">We can find its factor by quadratic formula. Formula to find factors is given as:</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">U = -b + √ (b<sup>2</sup> - 4ac) / 2a, here value of 'a' is 1, value of 'b' is ‘4’ and value of 'c' is ‘-10’. So put these values in formula. (know more about Polynomials , <a href="http://en.wikipedia.org/wiki/Polynomial">here</a>)</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">U = - 4 + √ [(4)<sup>2</sup> - 4(1) (-10)] / 2(1),</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">U = - 4 + √ (16 + 40) / 2,</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">U = - 4 + √ (56) / 2. So, we get two factor of this polynomial expression, one positive and other negative.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">U = -2 + √ 28 and U = -2 - √ 28.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">This is how we can find the factor.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong><a href="http://math.tutorvista.com/number-system/properties-of-square-roots.html">Square Root Property</a></strong> is one of the best method that is used to solve solutions to a quadratic equation. To get more information about square root property then follow <a href="http://boards.edurite.com/icse+board-syllabus~b1Uk.html">icse syllabus 2013</a>.</span></span></span></div><div style="margin-bottom: 0cm;"><br />
</div></div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-30873347201953071322012-08-06T03:35:00.002-07:002012-08-06T04:35:51.411-07:00polynomial factoring calculator<div dir="ltr" style="text-align: left;" trbidi="on"><span style="font-size: 10pt; line-height: 0.45cm;">Polynomial expression can be defined as any equation contain constant value, variables and exponent values joined by mathematical operators. Exponents values can be 0, 1, 2, 3, 4 and 5 ….etc. For example: 9xy</span><sup style="line-height: 0.45cm;">2</sup><span style="font-size: 10pt; line-height: 0.45cm;"> – 3x + 7y</span><sup style="line-height: 0.45cm;">3</sup><span style="font-size: 10pt; line-height: 0.45cm;"> – 20. In mathematics, Polynomial expression can also have negative and fraction values. It cannot be joined by division operator.</span><br />
<div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong><a href="http://www.tutorcircle.com/factoring-polynomials-calculator-ca4S9lc.html">Polynomial factoring calculator</a></strong> is a mathematical tool that help us to solve hard problem very easily. Those are unknown about polynomial factor can also find the factor of polynomial. Let’s understand some steps to find the factor of polynomial expression.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong>Step 1:</strong> First enter the polynomial expression in the text box.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong>Step 2:</strong> In other word put the coefficient of square, cube in one text box and coefficient of ‘x’ in other text box and the constant in last text box.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong>Step 3:</strong> Then enter the solve button to get the result.</span></span></span></div><div style="border-bottom-style: none; border-color: initial; border-left-style: none; border-right-style: none; border-top-style: none; border-width: initial; orphans: 2; padding-bottom: 0cm; padding-left: 0cm; padding-right: 0cm; padding-top: 0cm; widows: 2;"><span style="color: black; font-style: normal; font-weight: normal; line-height: 0.45cm;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Using these steps we can find the factor of polynomial expression. </span></span></span><span class="Apple-style-span" style="font-family: 'Lucida Grande', 'Lucida Sans Unicode', Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati; font-size: x-small;"><span class="Apple-style-span" style="line-height: 17px;">(know more about polynomial factoring calculator, <a href="http://en.wikipedia.org/wiki/Polynomial">here</a>)</span></span></div><div><br />
</div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Now we will understand how to find Factoring Polynomials. We can find the polynomial expressions factored by two methods i,e. direct method and by quadratic method. Here we will understand quadratic to find polynomial expressions.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">Let’s take a polynomial expression u<sup>2</sup> + u – 4, we can factorize this polynomial as mention below:</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">We can find its factor by quadratic formula. Formula to find factors is given as:</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">U = -b <u>+</u> √ (b<sup>2</sup> - 4ac) / 2a, here value of 'a' is given as 1, value of 'b' is given as ‘1’ and value of 'c' is given as ‘-4’. So put these values in formula.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">U = - 1 <u>+</u> √ [(1)<sup>2</sup> - 4(1) (-4)] / 2(1),</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">U = - 1 <u>+</u> √ (1 + 16) / 2,</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">U = - 1 <u>+</u> √ (17) / 2. So, here we get two factor of this expression, one positive and other negative.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">U = -1 + √ (17) / 2 and U = -1 - √ (17) / 2.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;">This is how we can find the factor.</span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati;"><span style="font-size: x-small;"><strong><a href="http://chemistry.tutorvista.com/biochemistry/antibiotics.html">Side effects of antibiotics</a></strong> may include a rash, swelling of the tongue etc. To get more information about side effect of antibiotics then follow <a href="http://boards.edurite.com/cbse+board-class+9-syllabus~beN-c2fs.html">cbse syllabus for class 9th</a>.</span></span></span></div><div style="border: none; line-height: 0.45cm; orphans: 2; padding: 0cm; widows: 2;"><br />
</div></div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-49671198777642387032012-07-06T02:21:00.001-07:002012-07-06T02:21:31.825-07:00prime factorization calculator<p>
<span style="font-size: small; line-height: 0.45cm; ">Prime factorization defines as a process in which a number is expressed in form of its prime factors. First we have to know about the prime factors that are numbers which have only two factors that are 1 and itself means numbers which are only divided by 1 and itself are known as prime numbers. So when we want to do prime factorization , It will be expressed in the multiplication form of prime numbers.</span></p>
<p align="LEFT" style="margin-bottom: 0cm; border: none; padding: 0cm; font-style: normal; font-weight: normal; line-height: 0.45cm; widows: 2; orphans: 2">
<font color="#000000"><font face="Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati"><font size="2"><span style="background: #ffffff">For process of prime factorization there is an on line tool that is known <strong>prime factorization calculator</strong>. It will help in calculation of prime factorization in easy and effective manner. It gives the perfect result quickly. It internally follow all the rules of prime factorization that is also called as integer factorization. We can calculate prime factorization of a number just by entering it into the text box of calculator and by clicking on the submit button. It provide the appropriate answer without delay.</span></font></font></font></p>
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<font color="#000000"><font face="Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati"><font size="2"><span style="background: #ffffff">It will be explained by an example as if there is a number 15 then prime factorization is calculated as divide the number by smallest prime number that will divide it that is 3 means 15 / 3 = 5 so first prime factor is 3 and 5 is itself a prime number so it can not be further divided, so prime factorization of 15 is 3 * 5. So it is a way of finding prime numbers that generate the original number when multiplied together.</span></font></font></font></p>
<p align="LEFT" style="margin-bottom: 0cm; border: none; padding: 0cm; font-style: normal; font-weight: normal; line-height: 0.45cm; widows: 2; orphans: 2">
<font color="#000000"><font face="Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati"><font size="2"><span style="background: #ffffff"><strong>Equation of a line</strong> is a type of linear equation that are expressed as y = m x + c in which x and y define coordinates of x and y axis and m and c are slope and intercept of a line respectively.</span></font></font></font></p>
<p align="LEFT" style="margin-bottom: 0cm; border: none; padding: 0cm; font-style: normal; font-weight: normal; line-height: 0.45cm; widows: 2; orphans: 2">
<font color="#000000"><font face="Lucida Grande, Lucida Sans Unicode, Calibri, Arial, Helvetica, Sans, FreeSans, Jamrul, Garuda, Kalimati"><font size="2"><span style="background: #ffffff">Each state in India have its own <strong>higher secondary education board</strong> that provides the quality education to their students and also organize the secondary and higher secondary exams. </span></font></font></font></p>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-56791400797658309572012-07-04T02:51:00.002-07:002012-07-05T05:52:10.074-07:00Prime Factorization Calculator<div dir="ltr" style="text-align: left;" trbidi="on"><span style="font-size: 9pt; line-height: 0.45cm;">Prime Factorization is the way of finding prime factors and prime factors are the numbers that are only divided by one or itself. These prime factors are whole numbers that are greater than one.</span><br />
<div align="LEFT" style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande,Lucida Sans Unicode,Calibri,Arial,Helvetica,Sans,FreeSans,Jamrul,Garuda,Kalimati;"><span style="font-size: x-small;"><span style="background: none repeat scroll 0% 0% rgb(255, 255, 255);">When we talk about the prime factorization it is describe as a process in which find the multiples of a given number that are in form of prime number.</span></span></span></span></div><div align="LEFT" style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande,Lucida Sans Unicode,Calibri,Arial,Helvetica,Sans,FreeSans,Jamrul,Garuda,Kalimati;"><span style="font-size: x-small;"><span style="background: none repeat scroll 0% 0% rgb(255, 255, 255);">We can explain it as 6 can be prime factorized as 2 * 3 .Both 2 and 3 are prime numbers and these are factors of 6 , so it is called as prime factorization. (want to Learn more about Prime Factorization, <a href="http://en.wikipedia.org/wiki/Prime_Factorization">click here</a>),</span></span></span></span></div><div align="LEFT" style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande,Lucida Sans Unicode,Calibri,Arial,Helvetica,Sans,FreeSans,Jamrul,Garuda,Kalimati;"><span style="font-size: x-small;"><span style="background: none repeat scroll 0% 0% rgb(255, 255, 255);">There is an on line tool that is known as <a href="http://www.tutorcircle.com/prime-factorization-calculator-with-steps-ca4Bflc.html"><b>Prime Factorization Calculator</b></a> used for calculation of prime factors of given number. In Prime Factorization Calculator there is a text box in which user enter number of their choice and calculator will find prime factorization easily and accurately. It is a very time efficient tool that provide the answer of given problem related to prime factorization quickly.</span></span></span></span></div><div align="LEFT" style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande,Lucida Sans Unicode,Calibri,Arial,Helvetica,Sans,FreeSans,Jamrul,Garuda,Kalimati;"><span style="font-size: x-small;"><span style="background: none repeat scroll 0% 0% rgb(255, 255, 255);">Internally it follows all the rules of finding the prime factorization. We can describe all the rules related with the process of prime factorization that are as follows:</span></span></span></span></div><div align="LEFT" style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande,Lucida Sans Unicode,Calibri,Arial,Helvetica,Sans,FreeSans,Jamrul,Garuda,Kalimati;"><span style="font-size: x-small;"><span style="background: none repeat scroll 0% 0% rgb(255, 255, 255);">In the first step check that by which number given value is divided by using the division rule.</span></span></span></span></div><div align="LEFT" style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande,Lucida Sans Unicode,Calibri,Arial,Helvetica,Sans,FreeSans,Jamrul,Garuda,Kalimati;"><span style="font-size: x-small;"><span style="background: none repeat scroll 0% 0% rgb(255, 255, 255);">And in next step divide number and check whether quotient is prime or not ,if not then it will further divided by the prime number using the division rule.</span></span></span></span></div><div align="LEFT" style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande,Lucida Sans Unicode,Calibri,Arial,Helvetica,Sans,FreeSans,Jamrul,Garuda,Kalimati;"><span style="font-size: x-small;"><span style="background: none repeat scroll 0% 0% rgb(255, 255, 255);">At last when the generated quotient is a prime number than show all prime factors in multiplication form.</span></span></span></span></div><div style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande,Lucida Sans Unicode,Calibri,Arial,Helvetica,Sans,FreeSans,Jamrul,Garuda,Kalimati;"><span style="font-size: x-small;"><span style="background: none repeat scroll 0% 0% rgb(255, 255, 255);">If we have a number 12 then it prime factors are first divide it with 2 that gives 6 and it is also divide by 2 that gives 3 and 3 is prime number and it will not further divided so the prime factorization of 12 is 2 * 2 * 3.</span></span></span></span></div><div align="LEFT" style="border: none; font-style: normal; font-weight: normal; line-height: 0.45cm; margin-bottom: 0cm; orphans: 2; padding: 0cm; widows: 2;"><span style="color: black;"><span style="font-family: Lucida Grande,Lucida Sans Unicode,Calibri,Arial,Helvetica,Sans,FreeSans,Jamrul,Garuda,Kalimati;"><span style="font-size: x-small;"><span style="background: none repeat scroll 0% 0% rgb(255, 255, 255);"><a href="http://math.tutorvista.com/algebra/simplifying-expressions.html"><b>Simplify the expression</b></a> is the process of solving given expression into the more simpler from that is easy to understand. <a href="http://boards.edurite.com/cbse+board-book%7EbeN.html"><b>cbse board books</b></a> are extremely beneficial for the preparation of engineering and medical examination. </span></span></span></span></div><div style="margin-bottom: 0cm;"><br />
</div></div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-9548036630568269362012-06-28T23:27:00.002-07:002012-06-29T03:05:15.573-07:00Steps to Factor Trinomials<div dir="ltr" style="text-align: left;" trbidi="on"><style type="text/css">
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In the previous post we have discussed about <a href="http://polynomial-trimonial-binomial.blogspot.in/2012/06/polynomial-long-division.html">Polynomial Long Division</a> and In today's session we are going to discuss about Steps to Factor Trinomials and How To Factor Trinomials Step By Step,<br />
1. Firstly we are going to compare the given trinomial with the standard form of the trinomial i.e. ax>2 + bx + c and recognize the values of a, b, and c.<br />
2. Now we are going to first look for the factor which is common in all the three terms. Once the common factor is recognized, we will bring it out of the three terms.<br />
3. In the next step, we will split the middle term in such a way that the product of the two splitted terms will be equal to the product of the first and the third term and the sum will be equal to the middle term.<br />
4. Further we will take out the common terms and make the factors.<br />
Let us take the following trinomial :<br />
18x>2 + 48*x*y + 32y>2<br />
Here we will first take out the factor 2, from all the three terms and we get :<br />
= 2 * (9x>2 + 24 * x * y + 16y>2)<br />
= 2 * (3x)>2 + 2 * 3 * 4 * x * y + (4y )>2<br />
= 2 * 3x + 4y>2<br />
Thus we come to the observation that the step by step procedure must be followed in order to get the factorization of the trinomial.<br />
If we are able to recognize the factors directly, relating it to some of the identity, then it becomes more easy for us to factorize. In case the trinomial is<br />
4x>2 + 12x + 9<br />
= (2x)>2 + 2 * 2 * 3x + 3>2<br />
= (2x + 3 )>2<br />
= (2x + 3 ) *(2x + 3 )<br />
<a href="http://www.tutorvista.com/homework-help"><b>homework help online</b></a> is available in math <a href="http://www.tutornext.com/">tutorials</a>. Online <a href="http://boards.edurite.com/cbse+board-class+8-book%7EbeN-c2dl.html">cbse class 8 books</a> is also available.</div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-60217883688314734912012-06-20T04:20:00.002-07:002012-06-21T02:27:55.355-07:00Polynomial Long Division<div dir="ltr" style="text-align: left;" trbidi="on">In the previous post we have discussed about <span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><a href="http://polynomial-trimonial-binomial.blogspot.in/2012/06/degree-of-polynomial.html" style="color: #5dc2c0; text-decoration: none;">Degree of Polynomial</a><span class="Apple-style-span" style="font-size: 22px;"> </span></span>and In today's session we are going to discuss about Polynomial Long Division. In this blog we are going to discuss the <strong><a href="http://www.tutorcircle.com/long-division-polynomials-fepLq.html">Polynomial Long Division</a></strong>. An operation that is used to dividing a polynomial value with the polynomial value is called as polynomial long division. The process in which a value is dividing by the same value or lower degree is also known as polynomial Long Division. Polynomial long division is denoted the term that is added, subtract and multiplied. This equation 7xy<sup>2</sup> + 3x – 11 is the representation of the polynomial long division. The polynomial word came from the two words the first one is ‘poly’ and second one is ‘nomial’. Poly means 'many' and nomial means 'term'. By combining both the meaning we get the word I. e. many terms. Polynomial may be denotes constant, variables, and exponent values and we can combine them with addition, subtraction and multiplication operation. (know more about Polynomial long division, <a href="http://en.wikipedia.org/wiki/Polynomial_long_division">here</a>)<br />
Lets consider a polynomial p (n), D (n) where degree (D) < degree (p), then the quotient polynomial Q(n) and remainder polynomial R(n) with degree(R) < degree(D),<br />
P(n) = Q(n) + R(n) ⇒ P(n) = D(n) Q(n) + R(n),<br />
D(n) D(n)<br />
<br />
By following some steps we can easily find the polynomial long division.<br />
Step1: Firstly we need to focus on the higher coefficient term which is present in the equation.<br />
Step2: We need to multiply the divisor with the leading term by doing that we can get coefficient term that will be exact.<br />
Step3: After getting the coefficient term we only have to change the sign of the variable. If negative sign is present, then we change it into positive sign and vice-versa.<br />
Step4 : At last cancel the term of same coefficient or variable.<br />
<br />
In <strong><a href="http://math.tutorvista.com/calculus/differential-equation-solver.html">differential equation solver</a></strong> we use some methods and somewhere it is related to the concept of how compound interest works. <strong><a href="http://boards.edurite.com/icse+board~b1Uk.html">Indian Certificate of Secondary Education</a></strong> is a type of exam that is comes under the Council for the Indian School Certificate Examinations. <br />
</div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-10460489596703456272012-06-19T01:15:00.002-07:002012-06-20T01:36:21.122-07:00Degree of Polynomial<div dir="ltr" style="text-align: left;" trbidi="on">In the previous post we have discussed about <span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><a href="http://polynomial-trimonial-binomial.blogspot.in/2012/06/how-to-deal-with-polynomials.html" style="color: #249fa3; text-decoration: none;">How to deal with Polynomials</a><span class="Apple-style-span" style="font-size: 22px;"> </span></span>and In today's session we are going to discuss about Degree of Polynomial. We know that the polynomial is the combination of the terms joined together with the sign of addition or subtraction. (know more about Polynomial,<a href="http://en.wikipedia.org/wiki/Polynomial"> here</a>)<br />
If the Polynomial has only one term we call it a monomial. If there are two terms in the polynomial, then we say that the polynomial is called the binomial and the polynomial with three terms is called trinomial. The polynomial with more than three terms is simply called the polynomial. By the term <strong><a href="http://www.tutorcircle.com/degree-of-polynomials-fejqq.html">degree of polynomial</a></strong>, we mean the highest power of the term among all the terms in the given expression. If we have the polynomial 2x + 3x>2 + 5 x>4, then we say that the term 5x>4 has the highest power. SO we say that the degree of the polynomial 2x + 3x>2 + 5 x>4, is 4. On the other hand if we have the polynomial 4x + 3, here the degree of thee polynomial is 1 as the power of x in 4x is maximum, which is equal to 1.<br />
We must remember that if the degree of the polynomial is 1, then we call the polynomial as the linear polynomial. In case the degree is 2, then the polynomial is quadratic polynomial and if the degree of the polynomial is 3, then the polynomial is called the conical polynomial. Here we write 2x + 5 is a linear polynomial, 5x>2 + 2x +5 is a quadratic polynomial; and 2x>3 + 5x>2 + 4x + 8 is a cubical polynomial.<br />
To learn more about the<a href="http://math.tutorvista.com/calculus/green-s-theorem.html"> <strong>Green s Theorem</strong></a>, we can take the help from the online math tutor and understand the concept of the lesson clearly. The sample papers of <strong><a href="http://boards.edurite.com/andhra+pradesh+board~bzV.html">Andhra Pradesh board of secondary education</a></strong> are available online to learn about the patterns of the Question paper which will be very useful to prepare about the exams.<br />
</div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-31691374051400838182012-06-18T04:02:00.002-07:002012-06-18T05:58:48.895-07:00How to deal with Polynomials<div dir="ltr" style="text-align: left;" trbidi="on">In the previous post we have discussed about <span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><a href="http://polynomial-trimonial-binomial.blogspot.in/2012/06/factoring-trinomials_16.html" style="color: #249fa3; text-decoration: none;">Factoring Trinomials</a><span class="Apple-style-span" style="font-size: 22px;"> </span></span>and In today's session we are going to discuss about How to deal with Polynomials. In mathematics, there is a term algebra in which we studied about the statements that express the relationship between the things. In the algebraic notation, relationship between the things can be described as a relationship between the variables and operators that are vary over time. In the same aspect <strong><a href="http://www.tutorcircle.com/polynomial-t2fsp.html">polynomials</a></strong> also consider as a part of algebra that deals with the real numbers and variables. Through the polynomials we can simply perform the basic operation like addition, subtraction and multiplication with the variables. In a more appropriate way we can say that polynomial is a combination of different types of terms with different mathematical operators. (know more about Polynomial ,<a href="http://en.wikipedia.org/wiki/Polynomials"> here</a>)<br />
In the standard definition we can say that polynomial is an expression that contains the combination of number and variable into it with basic operations and positive integer exponents. In the below we show how to we represent the polynomials into algebraic expression:<br />
3ab<sup>2</sup> – 4a + 6<br />
In the above given algebraic notation 3ab<sup>2</sup>, 4a, 6 can be consider as a terms through which we perform the basic operation that is addition and subtraction. In the above 3, 4 and 6 can be consider as a constants and ‘ab, a’ can be consider as variables. The power of two with the variable ab can be consider as positive exponents. In the other aspect exponents value describe the degree of the term. It means in above notation the term 3ab2 has a degree of 2. In the absence of exponent value we can take the degree of term as a one. Basically in mathematics polynomials are used for describing relationship between the numbers, variables and operations that generate some values. The output of polynomial expression helps the students to get the value of unknown variables. In the study of algebraic expression the concept of polynomial can be categorized into three categories that is monomial, binomial and trinomial. In mathematics <a href="http://math.tutorvista.com/calculus/definite-integrals.html"><strong>Definite Integral</strong> </a>can be consider as part of calculus which is used to integrate the function's values between upper limit to lower limit. The <strong><a href="http://boards.edurite.com/icse+board-book~b1Uk.html">ICSE board books</a></strong> help the students to make their study according to their syllabus that are conducted by the Indian certificate of secondary education.<br />
</div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-41773741225050815082012-06-16T05:06:00.001-07:002012-06-16T05:06:25.375-07:00Factoring Trinomials<p>
We know that the trinomial is the polynomial formed by three terms. To learn about <strong>Factoring Trinomials</strong>, we say that the standard form of the trinomial is ax>2 + bx + c.</p>
<p>
To find the factors of the above given polynomial , we say that we will either write it in form of some or the other identity or we will try to factorize it by the splitting method. In the splitting method, we say that the middle term of the trinomial is split in such a way that the sum of the two terms is equal to bx (i.e. the second term) and the product of the two split term is equal to the product of the first and the third term of the trinomial.</p>
<p>
Let us look at the following examples:</p>
<p>
If we have the polynomial: 4x>2 + 12x + 9</p>
<p>
Here we can write the above given polynomial as ( 2x )>2 + 2 * 2x * 3 + 3>2</p>
<p>
We observe that the above given polynomial is in the form of the identity (a + b) >2 = a>2 + 2 * a * b + b>2</p>
<p>
So it can be written as (2x + 3) >2</p>
<p>
If we solve the polynomial by splitting the second term we say it can be written as :</p>
<p>
4x>2 + 6x + 6x + 9</p>
<p>
= 2x * ( 2x + 3 ) + 3 * ( 2x + 3 )</p>
<p>
= ( 2x + 3 ) * ( 2x + 3 ) = ( 2x + 3 ) >2 Ans</p>
<p>
We will learn about <strong>Function Notation</strong>, by visiting the online math tutors and understand the concept related to this topic. We can also download <strong>Previous Year Question Papers Of CBSE</strong> for the particular subject and it will help us to have a look on the pattern of the previous year question papers.</p>
<p>
</p>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-37563802360933538742012-06-16T04:19:00.001-07:002012-06-16T04:20:02.147-07:00Factoring Trinomials<p>
We know that the trinomial is the polynomial formed by three terms. To learn about <strong>Factoring Trinomials</strong>, we say that the standard form of the trinomial is ax>2 + bx + c.</p>
<p>
To find the factors of the above given polynomial , we say that we will either write it in form of some or the other identity or we will try to factorize it by the splitting method. In the splitting method, we say that the middle term of the trinomial is split in such a way that the sum of the two terms is equal to bx (i.e. the second term) and the product of the two split term is equal to the product of the first and the third term of the trinomial.</p>
<p>
Let us look at the following examples:</p>
<p>
If we have the polynomial: 4x>2 + 12x + 9</p>
<p>
Here we can write the above given polynomial as ( 2x )>2 + 2 * 2x * 3 + 3>2</p>
<p>
We observe that the above given polynomial is in the form of the identity (a + b) >2 = a>2 + 2 * a * b + b>2</p>
<p>
So it can be written as (2x + 3) >2</p>
<p>
If we solve the polynomial by splitting the second term we say it can be written as :</p>
<p>
4x>2 + 6x + 6x + 9</p>
<p>
= 2x * ( 2x + 3 ) + 3 * ( 2x + 3 )</p>
<p>
= ( 2x + 3 ) * ( 2x + 3 ) = ( 2x + 3 ) >2 Ans</p>
<p>
We will learn about <strong>Function Notation</strong>, by visiting the online math tutors and understand the concept related to this topic. We can also download <strong>Previous Year Question Papers Of CBSE</strong> for the particular subject and it will help us to have a look on the pattern of the previous year question papers.</p>
<p>
</p>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-23263263903700136702012-06-07T22:20:00.002-07:002012-06-08T02:42:45.772-07:00How to use Gcd Calculator<div dir="ltr" style="text-align: left;" trbidi="on">In the previous post we have discussed about <span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><a href="http://polynomial-trimonial-binomial.blogspot.in/2012/06/how-to-use-lcm-calculator.html" style="color: #249fa3; text-decoration: none;">How to use LCM Calculator</a></span> and In today's session we are going to discuss about How to use Gcd Calculator, By GCD, we mean greatest common divisor. If we want to learn about the divisor of the given numbers, we mean that the greatest divisor, which is divisible by all the given numbers. To learn about gcd, we will first find the factors of the given numbers. We must ensure that the factors of the given number should be all prime factors. Now we will pick the factors of the given number such that they are common to both the numbers whose gcf is to be calculated. In case the gcf is one, the two numbers are not having any of the common factors. We use gcf to find the lowest form of the fraction numbers, rational numbers or the ratios. It simply signifies that the two numbers whose gcf is 1, cannot be divided by the same number. We must remember that the gcf of two prime numbers is always 1<br />
Suppose we want to find the gcf of 9 and 12<br />
Here we will first find the prime factors of 9 and 12. So we say that the prime factors of 9 = 3 * 3 * 1 and the prime factors of 12 = 2 * 2 * 3 * 1<br />
In both the prime factors we find that the numbers 1 and 3 are the prime factors of both the numbers. So 1 * 3 is the gcf of 9 and 12.<br />
We can also use <strong><a href="http://www.tutorcircle.com/gcd-calculator-ca2EOlc.html">gcd calculator</a></strong> to practice the problems based on gcd and understand its logics clearly. If we want to learn about the <strong><a href="http://math.tutorvista.com/statistics/central-tendency.html">Central Tendency</a></strong>, we can take online help from the math tutor which is available online every time. To know more about the contents of <strong><a href="http://boards.edurite.com/cbse+board-syllabus~beN.html">CBSE syllabus</a></strong> we will visit the site of CBSE and collect the recent information to update our self.<br />
</div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-79835913727971260322012-06-07T22:09:00.002-07:002012-06-08T02:05:12.912-07:00How to use LCM Calculator<div dir="ltr" style="text-align: left;" trbidi="on">Lcm stands for the least common multiple. By the term Lcm, we mean the process of finding the number, which is the least common multiple of all the given numbers. Let’s first see what is a multiple. By the word multiple, we mean that the number which exactly divides the given number. Thus if we say that 12 is the multiple of 3, it means that the number 3 completely divides the number 12.<br />
Now if we have to find the Lcm of the two numbers say 3 and 6, then we will first write the multiples of 3 and the multiples of 6, which are as follows :<br />
<br />
Multiples of 3 = 3 , 6 , 9, 12, 15, 18, 21, 24, . . . . . .<br />
Similarly, we have the multiples of 6 = 6, 12, 18, 24, . . . . . .<br />
Now we will observe the common multiples of the two numbers 3 and 6 as 6, 12, 18, 24, 30 . . . . which means that these numbers divides both the numbers completely. Out of these numbers we say that the number 6 is the smallest number. So we come to the conclusion that 6 is the L.C. M of the numbers 3 and 6.<br />
In the same way we can find the LCM of 3 or more numbers also. We must remember that the LCM of 1 and any number n is n itself.<br />
<br />
We can also download<a href="http://www.tutorcircle.com/lcm-calculator-ca2VIlc.html"> <strong>Lcm Calculator</strong></a> or use it online to understand the concepts of Lcm. To understand the concept of the <strong><a href="http://math.tutorvista.com/statistics/circle-graphs.html">Circle Graph</a>,</strong> we can study and learn from the books of CBSE or take the help of online math tutor. We also have <strong><a href="http://boards.edurite.com/cbse+board-sample-question-paper~beN.html">CBSE Sample Paper</a></strong> online which the students can download and use as a guidance tool for the students preparing for the exams and in the next session we will discuss about <span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><a href="http://polynomial-trimonial-binomial.blogspot.in/2012/06/how-to-use-gcd-calculator.html" style="color: #249fa3; text-decoration: none;">How to use Gcd Calculator</a>.</span><br />
</div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-67242185503888295882012-06-04T00:16:00.003-07:002012-06-08T03:29:17.641-07:00Least Common Denominator<div dir="ltr" style="text-align: left;" trbidi="on"> In today's session we are going to discuss about Least Common Denominator, By <strong><a href="http://www.tutorcircle.com/least-common-denominator-t7PYp.html">Least Common Denominator</a></strong>, we mean the LCM of the denominators of given fractions. Before we learn about Least Common Denominator, let us quickly recall the terms LCM, fractions & denominator; we are already familiar with. By LCM, we mean lowest common denominator. It can be calculated for 2 or more numbers by long division, listing of multiples of the given numbers or in the best way, by prime factorization. Now, fractions are numbers in the form a/b . A fraction, as we can see in the expression, has two parts, a & b. Here, a is the numerator & b is the denominator of the fraction. Thus, we have recalled denominator also that it is the lower part in the fraction.<br />
Now coming back to the topic of discussion, i.e. , Least Common Denominator or LCD ; as stated above is the LCM of the denominators of two or more fractions . But why do we need to find such LCD. As we know that the fractions may be like or unlike depending on whether their denominator is same or not & also that to add or subtract fractions; the fractions must be like fractions. If the fractions to be added or subtracted are like, we can add or subtract them easily. But for unlike fractions, we need to make them like by changing their denominators to Least Common Denominator. This is done by finding the LCM of the denominators of all unlike fractions. As for example; if we have to add 3/7+2/5+4/3. Here the fractions are unlike. So we’ll find the LCM of their denominators which comes out 105. Now we can change the fractions & make their denominator 105 by finding equivalent fractions. Thus, finally we have 3/7+2/5+4/3 = (45+42+140)/105=227/105. You can find the <strong><a href="http://math.tutorvista.com/algebra/independent-variables.html">Independent Variable Definition</a></strong> at different places online . Also look for <strong><a href="http://boards.edurite.com/icse+board-class+10-syllabus~b1Uk-cMB.html">ICSE class 10 syllabus</a></strong> online and in next session we will discuss about <span class="Apple-style-span" style="color: #222222; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif;"><a href="http://polynomial-trimonial-binomial.blogspot.in/2012/06/how-to-use-lcm-calculator.html" style="color: #249fa3; text-decoration: none;">How to use LCM Calculator</a>.</span></div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-31708336436736383702012-06-02T04:17:00.002-07:002012-06-04T01:18:40.349-07:00Adding Fractions Calculator<div dir="ltr" style="text-align: left;" trbidi="on">Fractions are the numbers which can be expressed in the form a/b , where a is called the numerator & b is called the denominator of the fraction . Numbers, in Mathematical terms can be added, subtracted, multiplied & even divided. Thus, we can do any of these on fractions as well; they being numbers. Here, we will learn about <a href="http://www.tutorcircle.com/adding-fractions-calculator-caSWlc.html"><b>Adding Fractions Calculator</b></a>.<br />
As we are already familiar with the term addition of numbers, we will extend the same to addition of fractions now. Addition means more or something increased by. So, when we add fractions, we increase them actually of find a fraction one more than the other.<br />
Now let us recall that fractions may be like or unlike depending whether the denominator of the given fractions is same or not. If the fractions have same denominator, we call them like fractions; else they are unlike fractions.<br />
Adding like fractions is quite simple. We just have to add the numerators of the fractions to be added & give the denominator of the fractions given to the sum of numerators so obtained. Thus, if we have to add 5/9 & 2/9 , we observe that the fractions are like . So, we will just add the numerators and we get 5/9 + 2/9 = (5+2)/9 =7/9.<br />
But, when we have to add unlike fractions, we first need to find the LCM of the denominators of the fractions to be added; thereafter making the given fractions like by taking their equivalent fractions with LCM as the denominator of all the fractions to be added. Next, we proceed like addition of like fractions. e.g., 1/6 + 2/5; these are unlike fractions & the LCM of denominators 6,5 is 30. Thus, changing the fractions to those with denominator 30, we get 1/6=5/30 & 2/5=12/30. Now, adding them we get 1/6+2/5=5/30+12/30 = (5+12)/30=17/30<br />
You can get more on <a href="http://math.tutorvista.com/number-system/simplifying-fractions.html"><b>simplifying fractions</b></a> online. Also <a href="http://boards.edurite.com/icse+board-class+12-sample-question-paper%7Eb1Uk-cgU.html"><b>class 12 icse sample papers</b></a> are available online.<br />
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</div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-15393635402488874982012-05-25T03:47:00.002-07:002012-05-28T00:43:04.059-07:00How to deal with factoring trinomials worksheet<div dir="ltr" style="text-align: left;" trbidi="on">To understand about <a href="http://www.tutorcircle.com/factoring-perfect-square-trinomials-worksheet-wst-323.html"><b>factoring trinomials worksheet</b></a>, we will first learn about what are trinomials. Trinomials are the polynomials, which has three terms. To find the factors of the trinomials, say ax>2 + bx + c we will first break the middle term bx such that the sum of the two terms is equal to bx and the product of the two spitted terms equals to the product of ax>2 and c. Once the middle term is split into two parts, we observe that the polynomial now has 4 terms. Now we take common terms from the first two terms and similarly we take common from last two terms in such a way that we are left with the common terms in the brackets. Thus taking the common terms common, we get the factors of the given polynomial. (want to Learn more about trinomials , <a href="http://en.wikipedia.org/wiki/Trinomial">click here</a>),<br />
Sometimes we have the trinomials such that it forms the perfect squares of the given terms, in such situation we will write the terms in the forms of the perfect squares. Let us try some of the examples: 4x>2 + 12x + 9<br />
= (2x)>2 + 2 * 2 * 3 * x + (3)>2<br />
It is equivalent to the formula for (a + b ) >2, so that a = 2x and b = 3, so the resultant factors of the equation are<br />
= ( 2x + 3 ) >2<br />
This solution can also be attained by the method of breaking, which is done as follows:<br />
= 4 x >2 + 6x + 6x + 9<br />
= 2x * ( 2x + 3 ) + 3 ( 2x + 3 )<br />
= ( 2x + 3) * ( 2x + 3 )<br />
To learn more about the <b><a href="http://math.tutorvista.com/statistics/box-and-whisker-plot.html">Box and Whisker Plot Definition</a>,</b> you need to take the help from online tutors. The detailed curriculum of <a href="http://boards.edurite.com/andhra+pradesh+board%7EbzV.html"><b>ap state education board</b></a> for different grades is available online.<br />
<br />
In the next session we will discuss about <a href="http://polynomial-trimonial-binomial.blogspot.in/2012/02/binomial-experiments.html">Binomial Experiments</a> and Read more maths topics of different grades such as <a href="http://number-system-and-conversion.blogspot.in/2012/05/subtracting-integers-worksheet.html">subtracting integers worksheet</a> in the upcoming sessions here. </div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-46356727068901608012012-05-22T02:46:00.002-07:002012-05-28T00:32:56.285-07:00factor algebra calculator<div dir="ltr" style="text-align: left;" trbidi="on">If we talk about algebra then you always need to deal with factors, factors can be done easily you need to have good knowledge of divisibility rule. If you are going to do the factor of any number then the first thing you need to notice is that the number is divisible by any number or not . We can make the <a href="http://www.tutorcircle.com/algebra-factoring-calculator-ca1bXlc.html"><b>factor algebra calculator</b></a> by factoring any number but as I told you earlier that you also need to have knowledge about divisibility rule. If a number has 0, 1,2,4,6,8 at its end then it is divisible by 2. If you add the digit and the sum is a factor of three then the number will be divisible by 3, if the last two digit of any number is divisible by four then the whole number is divisible by 4. And if a number contain the end digit as 0 and 5 then number is divisible by 5. In this way we can find the factor of any given number , now if we find the factor of 126 then this number contains 6 at the end so it is a factor of two but when we divide it by two the resulting number will be 63 , now it doesn’t contain a even number at the end so now 2 will not be the factor if we see the sum of the number is 6 + 3 =9 and 9 is divisible by 3 so three will be the factor, if we divide 63 by 3 we have 21 , now 21 is again divisible by 3, so if we divide 21 by 3 we will have 7 and as we know that seven is a prime number so only 7 will be the factor. So required factors are 2, 3, 3, and 7. Factors play a very important role in solving <a href="http://math.tutorvista.com/algebra/algebraic-equations.html"><b>Algebra Problems</b></a>. As the tamilnadu board exams are near so u need to buy <a href="http://boards.edurite.com/tamilnadu+board-sociology-sample-question-paper%7EbKu-sXa.html"><b>Tamilnadu Board Sociology Sample Papers</b></a> from the nearest shop.<br />
In the next session we will discuss about <a href="http://polynomial-trimonial-binomial.blogspot.in/2012/05/how-to-deal-with-factoring-trinomials.html">How to deal with factoring trinomials worksheet</a> and Read more maths topics of different grades such as <a href="http://number-system-and-conversion.blogspot.in/2012/03/properties-of-irrational-numbers.html">Properties of Irrational Numbers</a> in the upcoming sessions here. <br />
</div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-20121205262920871952012-02-27T22:35:00.002-08:002012-05-27T23:58:05.440-07:00Perfect Square Trinomials<div dir="ltr" style="text-align: left;" trbidi="on">Hello friends. Previously we have discussed about <a href="http://www.tutorcircle.com/consecutive-exterior-angles-sgHki.html">consecutive exterior angles</a> and In today's session we are going to discuss about Perfect Square Trinomials which comes under <a href="http://boards.edurite.com/andhra+pradesh+board%7EbzV.html">school secondary board of andhra pradesh</a>, <b><br />
</b><br />
Perfect Square: It is a number whose square root is a rational number.<br />
Example:<br />
121 = 11<sup>2</sup><br />
121 is a perfect square of 11 which is a rational number.<br />
0, 1, 4, 9, 16, 25, 36, 49, 64, 81, etc all these are the perfect squares.<br />
The perfect squares can also be in the form of p/q<br />
Example:<br />
9/49, 16/81, etc are also perfect squares.<br />
<b>Trinomials</b>: In polynomial expression there can be many terms in an equation but in <a href="http://math.tutorvista.com/algebra/trinomial-factorization.html">factoring trinomials</a> there must have exactly three terms connected by a plus or a minus sign.<br />
Example:<br />
4m<sup>2</sup> – 3m + 2<br />
m<sup>2 </sup>+ 7m – 8<br />
Perfect Square Trinomial: It can be represented by the following formula x<sup>2 </sup>± 2xy ± y<sup>2 </sup>(in another way we can see this formula as the square of the binomials); such trinomials are called perfect square trinomials. Perfect square trinomials can be formed when a binomial is multiplied by itself.<br />
(x ±y)<sup>2</sup> = x<sup>2 </sup>± 2xy ± y<sup>2</sup><br />
X<sup>2</sup> + 18X + 9is an example of perfect square trinomials, it can be shown in the form of (x + 3)<sup>2</sup><br />
Let’s see what the outcome is when we square any binomial, take (x + y)<br />
(x +y)<sup>2</sup> =(x + y)(x + y) = x<sup>2 </sup>+ 2xy + y<sup>2</sup><br />
The square of a binomial expression gives rise to the following three terms:<br />
1. x<sup>2 </sup>as Square of the first term of binomial<br />
2. 2xy as Twice the product of two terms<br />
3. y<sup>2 </sup>as Square of the second term of binomial<br />
It going to be the same if there is minus sign in place of plus sign.<br />
But we have to check first whether a trinomial is a perfect square trinomial or not.<br />
In the next session we are going to discuss <a href="http://polynomial-trimonial-binomial.blogspot.in/2012/05/factor-algebra-calculator.html">factor algebra calculator</a><br />
and if anyone want to know about <a href="http://number-system-and-conversion.blogspot.in/2012/02/binary-numbers.html">Binary Numbers</a> then they can refer to Internet and text books for understanding it more precisely.<br />
.<br />
</div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-18294646959914234992012-02-27T02:51:00.002-08:002012-05-27T23:39:28.341-07:00Binomial Theorem<div dir="ltr" style="text-align: left;" trbidi="on">Previously we have discussed about <a href="http://www.tutorcircle.com/adding-and-subtracting-integers-worksheet-wst-2Pn.html">subtracting integers worksheet</a> and In today's session we are going to discuss about Binomial theorem which comes under <a href="http://boards.edurite.com/andhra+pradesh+board%7EbzV.html">board of secondary education ap</a>, It is defined as the algebraic expansion of the powers of a binomial expression . A binomial expression consists of two terms containing the positive or negative sign between them . For example: ( x + y ) or ( p / q<sup>2</sup> ) - ( k / q <sup>4</sup> ) etc .<br />
We can <b>explain Binomial theorem</b> as when the binomial expression have the power of ' n ' then it would be expand by the help of binomial theorem . It would be describe as ( 1 + a ) <sup>n</sup> = <span style="font-family: Liberation Serif,serif;">∑ </span><sup><span style="font-family: Liberation Serif,serif;">n</span></sup><sub><span style="font-family: Liberation Serif,serif;">r=0 </span></sub>c <sub>r</sub><sup>n</sup> x <sup>r </sup>.<br />
The above expansion can understand by an example as<br />
( p + q ) <sup>4 </sup>= p <sup>4</sup> + 4 p <sup>3</sup> q + 6 p <sup>2</sup> q <sup>2</sup> + 4 p q <sup>3</sup> + q <sup>4 .</sup>In the example binomial coefficient in the expansion of ( p + q ) <sup>4</sup> are define as the coefficient in expansion of ( x + 1 )<sup>n </sup>are c <sub>r </sub><sup>n </sup>or <sub>n </sub>c <sub>r</sub> or ( <sup>n</sup> <sub>r </sub>) .<sub> </sub>for finding the values of the coefficient Pascal's triangle is used .<br />
1<br />
<ol></ol> 1 1<br />
1 2 1<br />
1 3 3 1<br />
1 4 6 4 1<br />
1 5 10 10 5 1<br />
1 6 15 20 15 6 1<br />
But by calculating <a href="http://math.tutorvista.com/statistics/binomial-probability-formula.html">Binomial Probability Formula</a> for computing the numbers in the pascal triangle so that we can easily expand the formula easily without referring the triangle it is stated as :<br />
( a + 1 ) <sup>n </sup>= c <sup>n</sup> <sub>n </sub>a <sup>n </sup>+ c <sup>n</sup> <sub>n -1</sub>a <sup>n-1 </sup>+ c <sup>n</sup> <sub>n -2 </sub>a <sup>n-2 </sup>+ ….......+c <sup>n</sup><sub>2 </sub>a <sup>2 </sup>+ c <sup>n</sup><sub>1 </sub>a + c <sup>n</sup><sub>0 .</sub><br />
In the next session we are going to discuss <a href="http://polynomial-trimonial-binomial.blogspot.in/2012/02/perfect-square-trinomials.html">Perfect Square Trinomials </a><br />
and Read more maths topics of different grades such as <a href="http://number-system-and-conversion.blogspot.in/2012/02/properties-of-numbers.html">Properties of Numbers</a><br />
in the upcoming sessions here. <br />
<br />
.</div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-69168288307346699072012-02-23T02:15:00.002-08:002012-05-27T23:27:47.859-07:00Binomial Experiments<div dir="ltr" style="text-align: left;" trbidi="on">Hi friends,Previously we have discussed about <a href="http://www.tutorcircle.com/multiplying-polynomials-worksheet-wst-2VI.html">multiplying polynomials worksheet</a> and topic we are going to discuss today is <b>binomial experiments</b> which is a part of <a href="http://boards.edurite.com/andhra+pradesh+board%7EbzV.html">ap board of secondary education</a>. The binomial experiments are part of the algebra mathematics. The binomial experiments are experiments in which have four conditions.<br />
1 ) the number of trials are fix.<br />
2 ) each trial is independent to others.<br />
3 ) only two outcomes are possible.<br />
4 ) the probability of each outcomes are constant from trial to trial.<br />
These processes are performed with a fixed number of independent trials, each have two possible outcomes.<br />
The <b>binomial experiment examples</b>: tossing a coin 10 times and see how many heads occur; Asking 100 people and find the result, if they watch xyz news; rolling a dice and see if the number 6 appears. Examples of the experiments that are not binomial experiments: rolling a dice a 6 appears (in this not a fixed number of trials), asking to the 10 people and how old they are (this means at least not two outcomes).<br />
<a href="http://math.tutorvista.com/statistics/binomial-probability-formula.html">Binomial Probability</a> example:<br />
Two coins are tossed simultaneously 300 times and it is found that two heads appeared 135 times, one head appeared 111 times and no head appeared 54 times. If two coins are tossed at random, what is the probability of getting 1) 2 heads 2) 1 head 3) 0 head?<br />
Solution : total number of trials = 135.<br />
Number of times 1 head appears = 111.<br />
Number of times 0 head appears = 54.<br />
In a random toss of two coins, let e<sub>1</sub>, e<sub>2</sub>, e<sub>3</sub> be the events of getting 2 heads, 1 head, 0 head respectively. Then, 1) p(getting 2 heads)=p(e<sub>1</sub>)= number of times 2 heads appear / total number of trials.<br />
135 / 300 = 0.45<br />
2) p (getting 1 head)= p(e<sub>2</sub>)= number of times 1 heads appear / total number of trials.<br />
111 / 300=0.37<br />
3)p(getting 0 head)= p(e <sub>3 </sub>)= number of times no heads appear / total number of trials.<br />
54 / 300=0.18<br />
the possible outcomes are e<sub>1</sub>, e<sub>2</sub>, e<sub>3</sub> and p(e<sub>1</sub>), p(e<sub>2</sub>), p(e<sub>3</sub>)=(0.45+0.37+0.18)=1<br />
In the next session we are going to discuss<span class="post-labels"></span> <a href="http://polynomial-trimonial-binomial.blogspot.in/2012/02/binomial-theorem.html">Binomial Theorem</a> and if anyone want to know about <a href="http://number-system-and-conversion.blogspot.in/2012/02/properties-of-complex-numbers.html">Properties of Complex Numbers</a> then they can refer to Internet and text books for understanding it more precisely. <br />
<div class="post-outer"><div class="post hentry"><h3 class="post-title entry-title"> </h3></div></div><b>.</b></div>manjunathnoreply@blogger.com0tag:blogger.com,1999:blog-2525643419876534648.post-52805763690014397692012-02-22T22:27:00.003-08:002012-05-27T23:14:51.985-07:00Solving Binomial Expansion<div dir="ltr" style="text-align: left;" trbidi="on">In <a href="http://math.tutorvista.com/algebra.html">college algebra</a> is the part of arithmetic, which perform the calculation on the variables. In the algebra, expressions are written in the form polynomial which is a part of <a href="http://boards.edurite.com/andhra+pradesh+board%7EbzV.html">secondary board of education andhra pradesh</a>. The binomial polynomial (<a href="http://www.tutorcircle.com/polynomial-worksheet-tp2fs.html">polynomials worksheet</a>) contains two terms. These two terms can be considered as a collection of or arranging the two monomial with operators and brackets option. Through this session we are discussing about <b>Solving Binomial Expansion</b>. Dividing Polynomials can be defined as two variables which perform some expression or some operation. Like a<sup>2</sup> – b<sup>2</sup> = (a + b) (a – b)<br />
The algebra provides the lots of way to solve the binomial expression. In the mathematics to solve the binomial expression we use the concept of expansion of binomial theorem. Binomial theorem can generally be represented by the formula given by Blaise Pascal in the 17th century. The most generic example of binomial expression is given below:<br />
(a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup><br />
In the more general term binomial formula can be expressed as a:<br />
(a + b)<sup>n</sup> = ∑∞i=0 (n/i) a<sup>i</sup> b<sup>n-i</sup><br />
Here (n/i) is a binomial coefficient and ‘n’ is a real number.<br />
In the simple term binomial expression can be written as:<br />
(a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup><br />
(a + b)<sup>3</sup> = a<sup>3</sup> + 3a<sup>2</sup>b + 3ab<sup>2</sup> + b<sup>3</sup><br />
As same like binomial theorem formula can be written as:<br />
(a + b)<sup>n</sup> = a<sup>n</sup> + n(a<sup>n-1</sup> b<sup>1</sup>) + n(n-1)/2! (a<sup>n-2</sup> b<sup>2</sup>) + n(n-1) (n-2)/3! (a<sup>n-3</sup> b<sup>3</sup>)+……….+ b<sup>n</sup><br />
<br />
Here we will show you <b>binomial expansion examples</b> and how to solve the binomial expression. (Know more about Binomial Expansion in broad manner, <a href="http://en.wikipedia.org/wiki/Binomial_expansion">here</a>,)<br />
Example1: Solve the binomial given expression (a + 5)<sup>3</sup>.<br />
Solution: Given that (a + 5)<sup>3</sup>, as we can see that it’s a binomial expression. So this can be solved by following the binomial expansion formula:<br />
So, solution become in simplified formula:<br />
(a + 5)<sup>3</sup> = a<sup>5</sup> + 3x<sup>2</sup> (5) + 3x (5)<sup>2</sup> + 5<sup>3</sup> <br />
(a + 5)<sup>3 </sup>= a<sup>5</sup> + 15 x<sup>2</sup> + 75x + 125<br />
As clear from the above solution, we can easily solve the binomial related problems.<br />
In the next session we are going to discuss <a href="http://polynomial-trimonial-binomial.blogspot.in/2012/02/binomial-experiments.html">Binomial Experiment</a> and Read more maths topics of different grades such as <a href="http://number-system-and-conversion.blogspot.in/2012/02/how-to-do-estimate-quotients.html">How to do Estimate Quotients</a> in the upcoming sessions here.<br />
<div class="date-posts"><div class="post-outer"><div class="post hentry"><a href="http://polynomial-trimonial-binomial.blogspot.in/2012/02/binomial-experiments.html"></a><br />
<h3 class="post-title entry-title"></h3></div></div></div></div>manjunathnoreply@blogger.com0