Every irreducible Polynomial is primitive or irreducible constant

Question

Let $R$ be an UFD. Is it true that an irreducible polynomial $f \in R[T]$ is either:

• primitive
• $f \in R$ and irreducible in $R$ ?

Answer 1

Suppose $f \notin R$ and $f$ is not primitive. Then $f$ can be factored into its content and primitive polynomial, so $f$ is not irreducible.