# How do you factor z^3 + 2z^2 - 16z - 32 by grouping?

Jun 13, 2016

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

#### Explanation:

There are 4 terms, so group them into two group of two - make sure there is a PLUS sign between the groups.

$\left({z}^{3} + 2 {z}^{2}\right) + \left(- 16 z - 32\right) \text{ common factor from each pair}$
=${z}^{2} \left(z + 2\right) - 16 \left(z + 2\right) \text{ note -16 as the common factor}$
=$\left(z + 2\right) \left({z}^{2} - 16\right)$

=$\left(z + 2\right) \left(z + 4\right) \left(z - 4\right)$