因数 x^{12}+2x^6+1

解

因数

x^{12} + 2 x^{6} + 1

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

解答ステップ

x^{12} + 2 x^{6} + 1

u =

にする

x^{2}

= u^{6} + 2 u^{3} + 1

因数

u^{6} + 2 u^{3} + 1 : (u + 1) (u^{2} - u + 1) (u + 1) (u^{2} - u + 1)

= (u + 1) (u^{2} - u + 1) (u + 1) (u^{2} - u + 1)

代用を戻す

u = x^{2}

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

簡素化

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