# How do you show that x+7 is a factor of x^3-37x+84. Then factor completely?

##### 1 Answer
Mar 18, 2018

The completely factored form is $\left(x + 7\right) \left(x - 3\right) \left(x - 4\right)$.

#### Explanation:

You can use synthetic division. I'm not going to explain how to do synthetic division here, but this website has a really good explanation of how it works.

Now we have our polynomial as $\left(x + 7\right) \left({x}^{2} - 7 x + 12\right)$.

We can factor our quadratic using $- 3$ and $- 4$:

$\textcolor{w h i t e}{=} \left(x + 7\right) \left({x}^{2} - 7 x + 12\right)$

$= \left(x + 7\right) \left({x}^{2} - 3 x - 4 x + 12\right)$

$= \left(x + 7\right) \left(\left(x - 3\right) \left(x - 4\right)\right)$

$= \left(x + 7\right) \left(x - 3\right) \left(x - 4\right)$

This is the fully factored polynomial. Hope this helped!