Solve x^3-16x+10x^2-160

$$x ^ { 3 } - 16 x + 10 x ^ { 2 } - 160$$

Factor

$$\left(x-4\right)\left(x+4\right)\left(x+10\right)$$

Solution Steps

Do the grouping x^{3}-16x+10x^{2}-160=\left(x^{3}-16x\right)+\left(10x^{2}-160\right), and factor out x in the first and 10 in the second group.

$$x\left(x^{2}-16\right)+10\left(x^{2}-16\right)$$

Factor out common term x^{2}-16 by using distributive property.

$$\left(x^{2}-16\right)\left(x+10\right)$$

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.

$$\left(x-4\right)\left(x+4\right)\left(x+10\right)$$

Evaluate

$$\left(x+10\right)\left(x^{2}-16\right)$$