# How do you factor -18x ^ { 3} - 8x ^ { 2} + 6x?

Nov 9, 2017

Extract the variable first into a quadratic and the variable.

#### Explanation:

$- 18 {x}^{3} - 8 {x}^{2} + 6 x = x \times \left(- 18 {x}^{2} - 8 x + 6\right)$
$2 x \times \left(- 9 {x}^{2} - 4 x + 3\right)$

$x = 0$ is one solution, the others are found using the quadratic formula on the remaining part of the expression.

Nov 9, 2017

$2 x \left(- 9 {x}^{2} - 4 x + 3\right)$

#### Explanation:

You have to factor out the largest factor of every term in the trinomial. It turns out that $2 x$ factors evenly out of every term.

$2 x \left(- 9 {x}^{2}\right) + 2 x \left(- 4 x\right) + 2 x \left(3\right)$

Pulling the $2 x$ term out to the front gives

$2 x \left(- 9 {x}^{2} - 4 x + 3\right)$