## Divisibility for polynomials

This post provides the details for the Divisibility lesson. Let $F$ be a field and $f,g \in F[X]$. Definition 1 $f$ divides $g$, written $f|g$, if $g = hf$ for some $h ∈ F[X]$. We also say that $g$ is a multiple of $f$. If $\deg(f) \ge 1$, we say that $f$ is prime or…