因数 (x+1)^4-10(x+1)^2+9

解

因数

(x + 1)^{4} - 10 (x + 1)^{2} + 9

x (x + 2) (x + 4) (x - 2)

解答ステップ

(x + 1)^{4} - 10 (x + 1)^{2} + 9

u =

にする

(x + 1)^{2}

= u^{2} - 10 u + 9

因数

u^{2} - 10 u + 9 : (u - 1) (u - 9)

= (u - 1) (u - 9)

代用を戻す

u = (x + 1)^{2}

= ((x + 1)^{2} - 1) ((x + 1)^{2} - 9)

因数

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

= ((x + 1) + 1) ((x + 1) - 1) ((x + 1)^{2} - 9)

因数

(x + 1)^{2} - 9 : ((x + 1) + 3) ((x + 1) - 3)

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

改良

= x (x + 2) (x + 4) (x - 2)