因数 4x^4-9x^2-6x-1

解

因数

4 x^{4} - 9 x^{2} - 6 x - 1

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

解答ステップ

4 x^{4} - 9 x^{2} - 6 x - 1

因数

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

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

簡素化

4 x^{4} : (2 x^{2})^{2}

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

2乗の差の公式を適用する:

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

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

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

簡素化

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

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

因数

2 x^{2} + 3 x + 1 : (2 x + 1) (x + 1)

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