# How do you factor f(x)=2x^3-10x^2-8x+40?

May 14, 2016

$\left(x - 2\right)$ $\left(2 x - 10\right)$ $\left(x + 2\right)$

#### Explanation:

First, find a factor of $f \left(x\right)$

try $f \left(1\right)$

$f \left(1\right)$ = 24 therefore is not a factor

next try $f \left(2\right)$

$f \left(2\right)$ = 0 therefore $\left(x - 2\right)$ is a factor of $f \left(x\right) = 2 {x}^{3} - 10 {x}^{2} - 8 x - 40$

Now, divide $f \left(x\right) = 2 {x}^{3} - 10 {x}^{2} - 8 x - 40$ by $\left(x - 2\right)$ using long division.

= $\left(x - 2\right)$ $\left(2 {x}^{2} - 6 x - 20\right)$

Then simplify this so

= $\left(x - 2\right)$ $\left(2 x - 10\right)$ $\left(x + 2\right)$