因数 x^6-14x^4+49x^2-36

解

因数

x^{6} - 14 x^{4} + 49 x^{2} - 36

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

解答ステップ

x^{6} - 14 x^{4} + 49 x^{2} - 36

u =

にする

x^{2}

= u^{3} - 14 u^{2} + 49 u - 36

因数

u^{3} - 14 u^{2} + 49 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} - 4 : (x + 2) (x - 2)

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

因数

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

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