因数 4x^5-x^3+32x^2-8

解

因数

4 x^{5} - x^{3} + 32 x^{2} - 8

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

解答ステップ

4 x^{5} - x^{3} + 32 x^{2} - 8

= (4 x^{5} - x^{3}) + (32 x^{2} - 8)

x^{3}

を

4 x^{5} - x^{3} : x^{3} (4 x^{2} - 1)

からくくり出す

8

を

32 x^{2} - 8 : 8 (4 x^{2} - 1)

からくくり出す

= x^{3} (4 x^{2} - 1) + 8 (4 x^{2} - 1)

共通項をくくり出す

4 x^{2} - 1

= (4 x^{2} - 1) (x^{3} + 8)

因数

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

= (2 x + 1) (2 x - 1) (x^{3} + 8)

因数

x^{3} + 8 : (x + 2) (x^{2} - 2 x + 2^{2})

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

2^{2} = 4

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