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Let $F$ be a field and $F[X]$ denote the ring of polynomials over $F$ in a single variable $X$. For $f(X), g(X) \epsilon F[X]$ with $g(X) \neq 0$, show that there exist $q(X), r(X) \epsilon F[X]$ such that degree $(r(X)) < $ degree $(g(X))$ and $f(X) = q(X).g(X) + r(X)$.
asked Nov 25, 2017 by randomisation (1,920 points)  

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