# Synthetic Division (Ruffini's Rule)

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Ruffini's rule is a method that allows the rapid division of a polynomial by a binomial of the form , where is one of the roots of the polynomial.

Contributed by: Eugenio Bravo (March 2011)

Open content licensed under CC BY-NC-SA

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Synthetic division is a shortcut method for dividing a polynomial by a linear factor of the form , where r is a root of the polynomial. It can be used instead of the standard long division algorithm. This method reduces the polynomial and the linear factor into a set of numeric values. After these values are processed, the resulting set of numeric outputs is used to construct the polynomial quotient and the polynomial remainder.

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