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

Jan 26, 2016

$\left(x + 3\right)$ is not a factor of the expression

#### Explanation:

By the Factor Theorem, if $\left(x + 3\right)$ is a factor of the expression then $x = - 3$ will be a zero of the expression. We can test this by substituting $x = - 3$ into the expression.
$2 {\left(- 3\right)}^{4} + 5 {\left(- 3\right)}^{3} - 2 {\left(- 3\right)}^{2} + 5 \left(- 3\right) + \left(- 3\right)$
$= 162 - 135 - 18 - 15 - 3$
$= - 9 \ne 0$

Therefore $\left(x + 3\right)$ is not a factor of the expression.