Gauss's Lemma on Primitive Rational Polynomials

Theorem
Let $\Q$ be the field of rational numbers.

Let $\Q \sqbrk X$ be the ring of polynomials over $\Q$ in one indeterminate $X$.

Let $\map f X, \map g X \in \Q \sqbrk X$ be primitive polynomials.

Then their product $f g$ is also a primitive polynomial.

Also see

 * Content of Rational Polynomial is Multiplicative