Content of Polynomial is Multiplicative

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Content of Rational Polynomial is Multiplicative

Let $h \in \Q \sqbrk X$ be a polynomial with rational coefficients.

Let $\cont h$ denote the content of $h$.

Then for any polynomials $f, g \in \Q \sqbrk X$ with rational coefficients:

$\cont {f g} = \cont f \cont g$

Content of Polynomial in Dedekind Domain is Multiplicative

Let $R$ be a Dedekind domain.

Let $f, g \in R \sqbrk X$ be polynomials.

Let $\cont f$ denote the content of $f$.

Then $\cont {f g} = \cont f \cont g$ is the product of $\cont f$ and $\cont g$.