Content formula

Content formula: Let $R$ be a UFD and let $f,g\in R[x]$. Then the content satisfies

i.e., $\operatorname{cont}(fg)$ is associate to $\operatorname{cont}(f)\operatorname{cont}(g)$. In particular, the product of primitive polynomials is primitive.

Here content is computed in the polynomial ring over a UFD . The formula implies that the product of two primitive polynomials is primitive and is a standard ingredient in Gauss's content lemma .