primitive polynomial

《Algebra》 · 第 269 页 · Chapter V，Section 4「Unique factorization in polynomial rings」，Lemma 4.5

Let $R$ be a commutative ring and $f=a_0+a_1x+\cdots+a_dx^d\in R[x]$ as above. (1) $f$ is very primitive if and only if $(a_0,\ldots,a_d)=(1)$. (2) If $R$ is a UFD, then $f$ is primitive if and only if $\gcd(a_0,\ldots,a_d)=1$.