At a Glance - Factoring Polynomials
We've already talked about factoring expressions, or breaking them down into parts or factors. We practiced finding the greatest common factor (GCF) of a collection of terms, and pulling it out of an expression as if it were an impacted molar. Since polynomials are expressions, we can also find the greatest common factor of the terms of a polynomial. Have your anesthesia and forceps at the ready.
There are also some other factoring techniques we can use to break down a polynomial. The idea of factoring is to write a polynomial as a product of other smaller, more attractive polynomials. We know this makes us sound shallow, but we don't care if these smaller polynomials have good personalities. They only need to be really, really, ridiculously good-looking.
While the coefficients of polynomials can be any real numbers, usually when we talk about factoring polynomials we're breaking down polynomials with integer coefficients into products of other polynomials with integer coefficients.