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In mathematics, Ruffini's rule is an efficient technique for dividing a polynomial by a binomial of the form ''x'' − ''r''. It was described by Paolo Ruffini in 1804. Ruffini's rule is a special case of synthetic division when the divisor is a linear factor. ==Algorithm== The rule establishes a method for dividing the polynomial : by the binomial : to obtain the quotient polynomial :; The algorithm is in fact the long division of ''P''(''x'') by ''Q''(''x''). To divide ''P''(''x'') by ''Q''(''x''): 1. Take the coefficients of ''P''(''x'') and write them down in order. Then write ''r'' at the bottom left edge, just over the line: | an an-1 ... a1 a0 | r | ----|--------------------------------------------------------- | | 2. Pass the leftmost coefficient (''a''''n'') to the bottom, just under the line: | an an-1 ... a1 a0 | r | ----|--------------------------------------------------------- | an | | = bn-1 | 3. Multiply the rightmost number under the line by ''r'' and write it over the line and one position to the right: | an an-1 ... a1 a0 | r | bn-1r ----|--------------------------------------------------------- | an | | = bn-1 | 4. Add the two values just placed in the same column | an an-1 ... a1 a0 | r | bn-1r ----|--------------------------------------------------------- | an an-1+(bn-1r) | | = bn-1 = bn-2 | 5. Repeat steps 3 and 4 until no numbers remain | an an-1 ... a1 a0 | r | bn-1r ... b1r b0r ----|--------------------------------------------------------- | an an-1+(bn-1r) ... a1+b1r a0+b0r | | = bn-1 = bn-2 ... = b0 = s | The ''b'' values are the coefficients of the result (''R''(''x'')) polynomial, the degree of which is one less than that of ''P''(''x''). The final value obtained, ''s'', is the remainder. As shown in the polynomial remainder theorem, this remainder is equal to ''P''(''r''), the value of the polynomial at ''r''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ruffini's rule」の詳細全文を読む スポンサード リンク
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