Gauss's Lemma on Primitive Rational Polynomials

Rational Polynomial
Let $\Q \left[{X}\right]$ be the ring of polynomial forms over the field of rational numbers in the indeterminate $X$.

Let $f \left({X}\right), g \left({X}\right) \in \Q \left[{X}\right]$ be primitive polynomials.

Then the product of $f$ and $g$ is also a primitive polynomial.

General Ring
Let $R$ be a commutative ring with unity.

Let $f,g \in R[X]$ be primitive polynomials.

Then $fg$ is primitive.