ABSTRACT
Last chapter, we defined the integral domain F [x] of all polynomials with coefficients in a field F . In this section we will investigate how such polynomials factor.
We say that f(x) factors if there are two non-constant polynomials g(x) and h(x) such that f(x) = g(x) ·h(x). We also say that both g(x) and h(x) divide the polynomial f(x). But g(x) and h(x) may also factor into non-constant polynomials. We want to show that we can factor f(x) into polynomials that cannot be factored further. We also want to lay down the groundwork for showing that the polynomials produced by this factorization are in some sense uniquely determined.
