因数 x^{135}-x^{27}

解

因数

x^{135} - x^{27}

x^{27} (x^{2} + 1) (x + 1) (x - 1) (x^{8} + x^{4} + 1) (x^{24} + x^{12} + 1) (x^{72} + x^{36} + 1)

解答ステップ

x^{135} - x^{27}

共通項をくくり出す

x^{27} : x^{27} (x^{108} - 1)

= x^{27} (x^{108} - 1)

因数

x^{108} - 1 : (x^{2} + 1) (x + 1) (x - 1) (x^{8} + x^{4} + 1) (x^{24} + x^{12} + 1) (x^{72} + x^{36} + 1)

= x^{27} (x^{2} + 1) (x + 1) (x - 1) (x^{8} + x^{4} + 1) (x^{24} + x^{12} + 1) (x^{72} + x^{36} + 1)