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State/Additivity of polynomial degrees
Proposition: (Additivity of polynomial degrees) Suppose that $R$ is an integral domain, such as $\ZZ$ or $\RR$, for example. Suppose that $P(X)$ and $Q(X)$ are nonzero polynomials with coefficients in $R$.
Then, $deg(P(X) \cdot Q(X)) = deg(P(X)) + deg(Q(X))$.
The following statements and definitions rely on the material of this page: State/Root counting over a field
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