# How do you factor 16 - 2x^3?

Apr 8, 2018

The fully factored polynomial is $= - 2 \left(x - 2\right) \left({x}^{2} + 2 x + 4\right)$.

#### Explanation:

First, factor out the $2$:

$\textcolor{w h i t e}{=} 16 - 2 {x}^{3}$

$= 2 \left(8 - {x}^{3}\right)$

Then, use the difference of cubes factoring:

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

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

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

Lastly, reorder the factors so that $x$ is in the front of each one:

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

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

$= 2 \left(- 1 \cdot \left(x - 2\right)\right) \left({x}^{2} + 2 x + 4\right)$

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

That's as factored as it gets. Hope this helped!