Corollary 2

— Let d be a gcd off and g. (i) If $u \in K[X]$, du is a gcd of fu and gu. (ii) If $v \in K[X]$ is a divisor ($\neq 0$) of f and g, then $d/v$ is a gcd of $f/v$ and $g/v$. This follows from Prop. 12, (ii).