Saturday, 22 October 2011

How to Solve Polynomials

Polynomial expressions are the most common way of representing mathematical equations with multiple terns as the name polynomial suggests , Poly = “multiple” and nomial = ”terms ” Polynomial expressions includes variables with or without integer coefficient and constants related to each other by normal arithmetic operators to form an equation. The standard form of any polynomial equation is as:

cn xn+.....+ c2 x2+ c1x1+ c0x0,

here cn , …....c2, c1,c0 are constant coefficient terms and x is variable with n to 0 order of degree.

Polynomial functions consist of finite number of derivatives in it. Let's take an example of polynomial equations for better understanding:

5x2+ 2x + 3 = 4

x =2

x2+ x3=1

Every polynomial equation is called as n- order polynomial equation and the value of 'n' is the highest degree among all the derivatives in the equation.

So the equation first is said to be as 2 – order polynomial equation.

Polynomial is further described according to the present number of variables in the equation. Any polynomial equation is said to be monomial if it consist only one variable in it .

x2+ 5x =3

here 'x' is the only variable in the equation so above one is a monomial equation.

If polynomial equation consists of 2 variables than it is said to be as binomial and if 3 than as trinomial.

Like x2– y2= 3 ( a binomial equation or a equation with two monomials )

x3- 2y + z = 5 ( a trinomial with three variables (x, y, z))

While performing multiplication between two polynomial terms, it just get complicated. In that case you only have to sum the products of each term multiplied of first polynomial by each term of second polynomial as in the example below:

(x2+ y2) ( x + y) =3

x3+x2y +y2x + y3=3

it gives 3 order polynomial equation as x3+ y3+ xy2+ x2y = 3

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