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The quotient can be computed using the Horner scheme. If F is a field and f and g are polynomials in F[X] with g ≠ 0, then there exist polynomials q and r in F[X] with :f = q g + r and such that that the degree of r is smaller than the degree of g. The polynomials q and r are uniquely determined by f and g. This is called "division with remainder" or "long division" and shows that the ring F[X] is a [euclidean domain]?. |
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