Content of Polynomial is Multiplicative
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Theorem
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 $\cont g$.