因数 x^5-x^3+x^2-1

解

因数

x^{5} - x^{3} + x^{2} - 1

(x + 1)^{2} (x - 1) (x^{2} - x + 1)

解答ステップ

x^{5} - x^{3} + x^{2} - 1

= (x^{5} - x^{3}) + (x^{2} - 1)

x^{3}

を

x^{5} - x^{3} : x^{3} (x^{2} - 1)

からくくり出す

= x^{3} (x^{2} - 1) + (x^{2} - 1)

共通項をくくり出す

(x^{2} - 1) : (x^{2} - 1) (x^{3} + 1)

= (x^{2} - 1) (x^{3} + 1)

因数

x^{2} - 1 : (x + 1) (x - 1)

= (x + 1) (x - 1) (x^{3} + 1)

因数

x^{3} + 1 : (x + 1) (x^{2} - x + 1)

= (x + 1) (x - 1) (x + 1) (x^{2} - x + 1)

指数の規則を適用する:

aa = a^{2}

(x + 1) (x + 1) = (x + 1)^{2}

= (x + 1)^{2} (x - 1) (x^{2} - x + 1)