The Division Algorithm states that for any polynomials $f(x)$ and $g(x) \neq 0$, there exist unique polynomials $q(x)$ (quotient) and $r(x)$ (remainder) such that $f(x) = g(x)q(x) + r(x)$, where the degree of $r(x)$ is less than the degree of $g(x)$.
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