因数 (x+1)^4-5(x+1)^2+4

解

因数

(x + 1)^{4} - 5 (x + 1)^{2} + 4

x (x + 2) (x + 3) (x - 1)

解答ステップ

(x + 1)^{4} - 5 (x + 1)^{2} + 4

u =

にする

(x + 1)^{2}

= u^{2} - 5 u + 4

因数

u^{2} - 5 u + 4 : (u - 1) (u - 4)

= (u - 1) (u - 4)

代用を戻す

u = (x + 1)^{2}

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

因数

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

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

因数

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

= ((x + 1) + 1) ((x + 1) - 1) ((x + 1) + 2) ((x + 1) - 2)

改良

= x (x + 2) (x + 3) (x - 1)