Suppose $R$ is a UFD, with $F$ its field of fractions.
A usual corollary to Gauss' Lemma on the content of polynomials states that if $f(X)\in F[X]$ has a factorization $f(X)=g(X)h(X)$ in $F[X]$, then if $f(X)$ and $g(X)$ are primitive and in $R[X]$, then so is $h(X)$. Why is $h(X)$ necessarily in $R[X]$?