# How do you use the factor theorem to determine whether x-2 is a factor of x^3 + 2x^2 - 5x - 6?

Sep 8, 2016

$\left(x - 2\right)$ is a factor of ${x}^{3} + 2 {x}^{2} - 5 x - 6$.

#### Explanation:

According to factor theorem if $\left(x - a\right)$ is a factor of $f \left(x\right)$, then $f \left(a\right) = 0$.

Hence to determine whether $\left(x - 2\right)$ is a factor of ${x}^{3} + 2 {x}^{2} - 5 x - 6$ or not, one needs to find the value of $f \left(2\right)$.

As $f \left(x\right) = {x}^{3} + 2 {x}^{2} - 5 x - 6$,

f(2)=2^3+2×2^2-5×2-6

= $8 + 8 - 10 - 6$

=$0$

Hence, $\left(x - 2\right)$ is a factor of ${x}^{3} + 2 {x}^{2} - 5 x - 6$.