因数 (x-1)^4+(x-1)^2-6

解

因数

(x - 1)^{4} + (x - 1)^{2} - 6

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

解答ステップ

(x - 1)^{4} + (x - 1)^{2} - 6

u =

にする

(x - 1)^{2}

= u^{2} + u - 6

因数

u^{2} + u - 6 : (u - 2) (u + 3)

= (u - 2) (u + 3)

代用を戻す

u = (x - 1)^{2}

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

拡張

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

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

拡張

(x - 1)^{2} + 3 : x^{2} - 2 x + 4

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