# How do you factor the expression 2x³ -x² - 4x + 3?

Mar 17, 2016

$2 {x}^{3} - {x}^{2} - 4 x + 3 = \left(x - 1\right) \left(x - 1\right) \left(2 x + 3\right)$

#### Explanation:

First notice that the sum of the coefficients is zero.

That is: $2 - 1 - 4 + 3 = 0$

So $x = 1$ is a zero and $\left(x - 1\right)$ a factor:

$2 {x}^{3} - {x}^{2} - 4 x + 3 = \left(x - 1\right) \left(2 {x}^{2} + x - 3\right)$

Next notice that the sum of the coefficients of the remaining quadratic factor is also zero.

That is: $2 + 1 - 3 = 0$

So $x = 1$ is a zero and $\left(x - 1\right)$ a factor:

$2 {x}^{2} + x - 3 = \left(x - 1\right) \left(2 x + 3\right)$