因数 x^4-x^2-2x-1

解

因数

x^{4} - x^{2} - 2 x - 1

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

解答ステップ

x^{4} - x^{2} - 2 x - 1

因数

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

= x^{4} - (x + 1)^{2}

簡素化

x^{4} : (x^{2})^{2}

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

2乗の差の公式を適用する:

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

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

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

簡素化

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

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