# How do you factor completely 2x^7 - 32x^3?

Mar 8, 2018

Take out the greatest common factor first.

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

#### Explanation:

First, find the highest number that goes into both terms in the expression (in this case $2 {x}^{3}$).

Divide that out of both terms like so:

$2 {x}^{3} \left({x}^{4} - 16\right)$

Then you factor the remaining part as the difference of squares as normal.

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

And again:

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