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Let F be a field, and let f (x), g(x) ∈ F [x] be nonzero polynomials....

Let F be a field, and let f (x), g(x) ∈ F [x] be nonzero polynomials. Then it must be the case that deg(f (x)g(x)) = deg(f (x)) + deg(g(x)).
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