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

Jul 22, 2018

See below:

#### Explanation:

Let's say we have a function $f \left(x\right)$:

If $f \left(c\right) = 0$, then $x - c$ is a factor of $f \left(x\right)$.

We want to see if $x + 4$ is a factor, so we can essentially evaluate $f \left(- 4\right)$. If we get zero, it is a factor. If we don't, it isn't.

Let's evaluate this function at $x = - 4$:

$2 {\left(- 4\right)}^{3} + {\left(- 4\right)}^{2} - 25 \left(- 4\right) + 12 = 0$

We do indeed get zero, which means $x + 4$ is a factor of our polynomial.

Hope this helps!