Factoring Polynomials

Polynomials that are not prime can be expressed in a completely factored form. To completely factor a polynomial, you need to express it as a product of its greatest common monomial factor (if there is any other than 1) and of its other factors, all of which should be prime polynomials. It is also important to note that when factoring polynomials, each factor should be a polynomial whose numerical coefficients are integers.

Consider the polynomial 6ax + 9ay from the previous slide. The completely factored form of 6ax + 9ay is $3a(2x+3y).$ Note that $3a$ is the greatest common monomial factor and $(2x+3y)$ is a prime polynomial.

In the next sections, you will learn about how you can get the greatest common monomial factor, as well as the different techniques in factoring polynomials.