Definition:Divisor of Polynomial

Definition
Let $D$ be an integral domain.

Let $D \left[{x}\right]$ be the polynomial ring in one variable over $D$.

Let $f, g \in D \left[{x}\right]$ be polynomials.

Then:
 * $f$ divides $g$
 * $f$ is a divisor of $g$
 * $f$ is a factor of $g$
 * $g$ is divisible by $f$


 * $\exists h \in D \left[{x}\right] : g = f h$
 * $\exists h \in D \left[{x}\right] : g = f h$

This is denoted:
 * $f \divides g$

Generalizations

 * Definition:Divisor of Ring Element: see Ring of Polynomial Forms is Integral Domain