因数 2x^5-16x^3+x^2+24x-2

解

因数

2 x^{5} - 16 x^{3} + x^{2} + 24 x - 2

(x^{2} - 2) (2 x (x^{2} - 6) + 1)

解答ステップ

2 x^{5} - 16 x^{3} + x^{2} + 24 x - 2

指数の規則を適用する:

a^{b + c} = a^{b} a^{c}

x^{5} = x x^{4}, x^{3} = x x^{2}

= 2 x x^{4} - 16 x x^{2} + x^{2} + 24 x - 2

書き換え

= 2 x x^{4} - 8 \cdot 2 x x^{2} + x^{2} + 12 \cdot 2 x - 2

共通項をくくり出す

2 x

= 2 x (x^{4} - 8 x^{2} + 12) + x^{2} - 2

因数

x^{4} - 8 x^{2} + 12 : (x^{2} - 2) (x^{2} - 6)

= x^{2} + 2 x (x^{2} - 2) (x^{2} - 6) - 2

書き換え

= 2 (x^{2} - 2) x (x^{2} - 6) + 1 \cdot (x^{2} - 2)

共通項をくくり出す

(x^{2} - 2)

= (x^{2} - 2) (2 x (x^{2} - 6) + 1)