Solve h(x)=x^3+8x^2-9x-72

$$h ( x ) = x ^ { 3 } + 8 x ^ { 2 } - 9 x - 72$$

Factor

$$\left(x-3\right)\left(x+3\right)\left(x+8\right)$$

Solution Steps

Do the grouping x^{3}+8x^{2}-9x-72=\left(x^{3}+8x^{2}\right)+\left(-9x-72\right), and factor out x^{2} in the first and -9 in the second group.

$$x^{2}\left(x+8\right)-9\left(x+8\right)$$

Factor out common term x+8 by using distributive property.

$$\left(x+8\right)\left(x^{2}-9\right)$$

Consider x^{2}-9. Rewrite x^{2}-9 as x^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)$$

Rewrite the complete factored expression.

$$\left(x-3\right)\left(x+3\right)\left(x+8\right)$$

Evaluate

$$\left(x+8\right)\left(x^{2}-9\right)$$