# How do you use the factor theorem to determine whether x+4 is a factor of 2x^3 + x^2 - 25x + 12 ?

Jan 23, 2016

Since when $x = - 4$ then $2 {x}^{3} + {x}^{2} - 25 x + 12 = 0$
by the factor theorem $\left(x + 4\right)$ is a factor.

#### Explanation:

The factor theorem says that for an expression $f \left(x\right)$
then $\left(x - a\right)$ is a factor of $f \left(x\right)$ if and only if $f \left(a\right) = 0$

Note that $\left(x + 4\right) = \left(x - \textcolor{red}{\left(- 4\right)}\right)$

So we evaluate
color(white)("XXX")f(color(red)(-4)) = 2(-4)^3+-4)^2-25(-4)+12

$\textcolor{w h i t e}{\text{XXXXXXX}} = - 128 + 16 + 100 + 12$

$\textcolor{w h i t e}{\text{XXXXXXX}} = 0$

and discover that $\left(x - \left(- 4\right)\right) = \left(x + 4\right)$ is a factor of the given expression.