# How do you use the factor theorem to determine whether x+2 is a factor of x^4 - 3x - 5?

Dec 1, 2015

According to the Factor Theorem
$f \left(- 2\right) = 0$ if and only if $\left(x + 2\right)$ is a factor of $f \left(x\right)$

#### Explanation:

Given $f \left(x\right) = {x}^{4} - 3 x - 5$

$f \left(- 2\right) = {\left(- 2\right)}^{4} - 3 \cdot \left(- 2\right) - 5 = 16 + 6 - 5 = 17 \ne 0$

and therefore $\left(x + 2\right)$ is not a factor of $f \left(x\right) = {x}^{4} - 3 x - 5$