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''See also: Eisenstein criterion'' In algebra, the rational root theorem (or rational root test, rational zero theorem or rational zero test) states a constraint on rational solutions (or roots) of a polynomial equation : with integer coefficients. If ''a''0 and ''a''''n'' are nonzero, then each rational solution ''x'', when written as a fraction ''x'' = ''p''/''q'' in lowest terms (i.e., the greatest common divisor of ''p'' and ''q'' is 1), satisfies * ''p'' is an integer factor of the constant term ''a''0, and * ''q'' is an integer factor of the leading coefficient ''a''''n''. The rational root theorem is a special case (for a single linear factor) of Gauss's lemma on the factorization of polynomials. The integral root theorem is a special case of the rational root theorem if the leading coefficient ''a''''n'' = 1. == Proofs == 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「Rational root theorem」の詳細全文を読む スポンサード リンク
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