因数 x^6-6x^4-31x^2+36

解

因数

x^{6} - 6 x^{4} - 31 x^{2} + 36

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

解答ステップ

x^{6} - 6 x^{4} - 31 x^{2} + 36

u =

にする

x^{2}

= u^{3} - 6 u^{2} - 31 u + 36

因数

u^{3} - 6 u^{2} - 31 u + 36 : (u - 1) (u + 4) (u - 9)

= (u - 1) (u + 4) (u - 9)

代用を戻す

u = x^{2}

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

因数

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

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

因数

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

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