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In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalised version of the familiar arithmetic technique called long division. It can be done easily by hand, because it separates an otherwise complex division problem into smaller ones. Sometimes using a shorthand version called synthetic division is faster, with less writing and fewer calculations. Polynomial long division is an algorithm that implements the Euclidean division of polynomials, which starting from two polynomials ''A'' (the ''dividend'') and ''B'' (the ''divisor'') produces, if ''B'' is not zero, a ''quotient'' ''Q'' and a ''remainder'' ''R'' such that :''A'' = ''BQ'' + ''R'', and either ''R'' = 0 or the degree of ''R'' is lower than the degree of ''B''. These conditions define uniquely ''Q'' and ''R'', which means that ''Q'' and ''R'' do not depend on the method used to compute them. ==Example== Find the quotient and the remainder of the division of the ''dividend'', by the ''divisor''. The dividend is first rewritten like this: : The quotient and remainder can then be determined as follows: The polynomial above the bar is the quotient ''q''(''x''), and the number left over ( 5) is the remainder ''r''(''x''). : The long division algorithm for arithmetic is very similar to the above algorithm, in which the variable ''x'' is replaced by the specific number 10. 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「Polynomial long division」の詳細全文を読む スポンサード リンク
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