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# Algebra: Prove the uniqueness part of the division theorem for polynomial...(read on)

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1. Prove this:
Let g(X), p(X), q(X), r(X), s(X) ∈ F[X] with g(X) ≠ 0. Suppose that
q(X)g(X) + r(X) = p(X)g(X) + s(X),
and that r(X) = 0 or deg r(X) < deg g(X), and s(X) = 0 or deg s(X) < deg g(X). Then
p(X) = q(X) and r(X) = s(X).

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Updated: October 12, 2016
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