# How do you determine whether x+2 is a factor of the polynomial 2x^3-x^2-5x-8?

Feb 17, 2017

not a factor.

#### Explanation:

Using the $\textcolor{b l u e}{\text{Remainder rheorem}}$

$\text{If "(x+h)" is a factor then } P \left(- h\right) = 0$

$\text{for } \left(x + 2\right) , h = - 2$

$\Rightarrow 2 {x}^{3} - {x}^{2} - 5 x - 8$

=2(-2)^3-(-2)^2-5(-2)-8≠0

$\Rightarrow \left(x + 2\right) \text{ is not a factor of the polynomial}$