# How do you factor completely 2x^5 - 7x^3 - 4x?

Jul 17, 2016

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

#### Explanation:

Take out the common factor of $x$ first.

$x \left(2 {x}^{4} - 7 {x}^{2} - 4\right)$

We now have a disguised quadratic, but we treat it the same as a quadratic.

Find factors of 2 and 4 which subtract to make 7.

$\text{2 +1 "rArr " 1 x 1 = +1}$
$\text{1 -4 "rArr " 2 x 4 = -8 } \Rightarrow - 8 + 1 = - 7$

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