Polynomial divisibility

Dependencies:

1. Polynomial

A polynomial $p(x)$ is divisible in $F[x]$ by $q(x)$ iff there exists a polynomial $r(x)$ such that $p(x), q(x), r(x) \in F[x]$ and $p(x) = q(x)r(x)$.

Dependency for:

1. q(x)F[x] is in p(x)F[x] iff p(x) divides q(x)
2. Product of linear factors is a factor
3. F[x]/p(x): A ring
4. Gauss' Lemma

Info:

• Depth: 3
• Number of transitive dependencies: 3

Transitive dependencies:

1. Group
2. Ring
3. Polynomial