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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