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 $f(X) = q(X).g(X) + r(X)$.