因式分解 2x^3+7x^2-10x-24

解答

因式分解

2 x^{3} + 7 x^{2} - 10 x - 24

(x - 2) (2 x + 3) (x + 4)

求解步骤

2 x^{3} + 7 x^{2} - 10 x - 24

使用有理根定理

= (x - 2) \frac{2 x ^{3} + 7 x ^{2} - 10 x - 24}{x - 2}

\frac{2 x ^{3} + 7 x ^{2} - 10 x - 24}{x - 2} = 2 x^{2} + 11 x + 12

= (x - 2) (2 x^{2} + 11 x + 12)

因式分解

2 x^{2} + 11 x + 12 : (2 x + 3) (x + 4)

= (x - 2) (2 x + 3) (x + 4)