Past exam of the mathematics course of the University of Cambridge / 2018 / ib / Paper 3 / 11G / a

Gauss lemma for polynomials says that the product of two primitive polynomials in $\mathbb{Z}[X]$ is primitive. Equivalently, a primitive polynomial in $\mathbb{Z}[X]$ is reducible over $\mathbb{Q}$ exactly when it is reducible over $\mathbb{Z}$.