Solve x^3+2x^2-16x-32

$$x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32$$

Factor

$$\left(x-4\right)\left(x+2\right)\left(x+4\right)$$

Solution Steps

Do the grouping x^{3}+2x^{2}-16x-32=\left(x^{3}+2x^{2}\right)+\left(-16x-32\right), and factor out x^{2} in the first and -16 in the second group.

$$x^{2}\left(x+2\right)-16\left(x+2\right)$$

Factor out common term x+2 by using distributive property.

$$\left(x+2\right)\left(x^{2}-16\right)$$

Consider x^{2}-16. Rewrite x^{2}-16 as x^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4\right)\left(x+4\right)$$

Rewrite the complete factored expression.

$$\left(x-4\right)\left(x+2\right)\left(x+4\right)$$

Evaluate

$$\left(x+2\right)\left(x^{2}-16\right)$$