Associates in Ring of Polynomial Forms over Field

Theorem
Let $F \left[{X}\right]$ be the ring of polynomial forms over the field $F$.

Then $d \left({X}\right) \in F \left[{X}\right]$ is an associate of $d' \left({X}\right)$ iff $d \left({X}\right) = c \cdot d' \left({X}\right)$ for some $c \in F, c \ne 0$.

Hence any two polynomials in $F \left[{X}\right]$ have a unique monic GCD.