factor polynomials

In the previous post we have discussed about  How do you Determine if a Polynomial is the Difference of Two Squares 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.

We can factor polynomials and write them as the product of different expressions. There are different methods to find the factor of the given polynomials.

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 :

2x ( 2x + 1 ) .

Thus the given polynomial can be written as the product of 2x * ( 2x + 1 ).

Another method of finding the factors of the given polynomial is by breaking the middle term.

Let's us take the polynomial x>2 + 7x – 18:

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. (know more about factor polynomials, here)

Thus the given polynomial can be written as follows:

=2x>2 + 9x – 2x -18 ,

=2x>2 -2x + 9x -18,

= 2x (x – 1) + 9 (x – 1),

= (2x + 9) (x – 1) .

Some times the polynomial are similar to the standard identities, which can be directly written in their form.

For example if we have 9x>2 - 4y>2,

= (3x)>2 – (2y) >2 ,

=(3x – 2y ) (3x + 2y).

This solution is based on the identity a>2 – b>2 = ( a + b ) * ( a – b ) .

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How do you Determine if a Polynomial is the Difference of Two Squares

Hi friends, we will discuss How do you Determine if a Polynomial is the Difference of Two Squares. 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.

Now we will use some step to solve polynomial:
Step 1: To find polynomial first we need to solve the given expression. For example: suppose that we have given a polynomial expression 2p² + 2p² - 10 – 6. Now we have to solve it as 4p² – 16.
Step 2: 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 4².
Step 3: 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 p² – q².

Step 4: 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 4p² – 16 that is written in factorized form as (2p + 4) (2p - 4).

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How do you Determine if a Polynomial is the Difference of Two Squares

In the previous post we have discussed about Factoring Polynomials Calculator 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 How do you Determine if a Polynomial is the Difference of Two Squares. 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: 4ab² + 7xy² – 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, here)

Step 1: 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.

Step 2: If we want to calculate if a polynomial is the difference we need to subtract one polynomial value other polynomial value.

Step 3: Then we have to check the answer that it matches a given polynomial or not.

Step 4: 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: p² – q². 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:

= p² – q², on finding it factor we get:

= (p + q) (p – q), here we get the difference of two squares.

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.

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Factoring Polynomials Calculator

In the previous post we have discussed about polynomial factoring calculator 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 Factoring Polynomials Calculator. If in any equation constant value, variables and exponent values are present then it is polynomial expression. For example: 3xy² – 6x + 2y³– 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.

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.

Step 1: Put polynomial expression in first text box.

Step 2: Or enter coefficient of square, cube in one text box and coefficient of ‘x’ in next text box and constant in last text box.

Step 3: Then press solve button to get result.

By using the given steps we can calculate the factor of polynomial expression.

Now we will discuss how to find factor of polynomials expression. Here we will discuss quadratic method to find polynomial expressions.

Let’s have a polynomial expression u²+ 4u – 10, we can factorize this polynomial as shown below:

We can find its factor by quadratic formula. Formula to find factors is given as:

U = -b + √ (b² - 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 , here)

U = - 4 + √ [(4)² - 4(1) (-10)] / 2(1),

U = - 4 + √ (16 + 40) / 2,

U = - 4 + √ (56) / 2. So, we get two factor of this polynomial expression, one positive and other negative.

U = -2 + √ 28 and U = -2 - √ 28.

This is how we can find the factor.

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polynomial factoring calculator

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: 9xy² – 3x + 7y³ – 20. In mathematics, Polynomial expression can also have negative and fraction values. It cannot be joined by division operator.

Polynomial factoring calculator 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.

Step 1: First enter the polynomial expression in the text box.

Step 2: 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.

Step 3: Then enter the solve button to get the result.

Using these steps we can find the factor of polynomial expression. (know more about polynomial factoring calculator, here)

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.

Let’s take a polynomial expression u² + u – 4, we can factorize this polynomial as mention below:

We can find its factor by quadratic formula. Formula to find factors is given as:

U = -b + √ (b² - 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.

U = - 1 + √ [(1)² - 4(1) (-4)] / 2(1),

U = - 1 + √ (1 + 16) / 2,

U = - 1 + √ (17) / 2. So, here we get two factor of this expression, one positive and other negative.

U = -1 + √ (17) / 2 and U = -1 - √ (17) / 2.

This is how we can find the factor.

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