Solve 2x^3+8x^2-3x-12

$$2 x ^ { 3 } + 8 x ^ { 2 } - 3 x - 12$$

Factor

$$\left(x+4\right)\left(2x^{2}-3\right)$$

Solution Steps

Do the grouping 2x^{3}+8x^{2}-3x-12=\left(2x^{3}+8x^{2}\right)+\left(-3x-12\right), and factor out 2x^{2} in the first and -3 in the second group.

$$2x^{2}\left(x+4\right)-3\left(x+4\right)$$

Factor out common term x+4 by using distributive property. Polynomial 2x^{2}-3 is not factored since it does not have any rational roots.

$$\left(x+4\right)\left(2x^{2}-3\right)$$

Evaluate

$$\left(x+4\right)\left(2x^{2}-3\right)$$