Synthetic Division (Ruffini's Rule)
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.
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.