# How do you factor x^2-7x-18?

Nov 30, 2016

$\left(x - 9\right) \left(x + 2\right)$

#### Explanation:

First step, we need to split the equation up into factors that will multiply back into the given quadratic.

What times $x$ will yield ${x}^{2}$ ?

$x \cdot x$, of course.

So, that gives us factors of ${x}^{2}$

$\left(x \text{ ")(x" }\right)$

Now we need two numbers that will multiply into $- 18$ and subtract into $- 7$.

The factors of $18$ are $2 , 3 , 6 , 9$.

$\left(- 9\right) \left(+ 2\right) = - 18 \text{ }$ and $\text{ } - 9 + 2 = - 7$

Therefore

$= {x}^{2} - 7 - 18$

$= \left(x - 9\right) \left(x + 2\right)$

Always look for the operator signs as a helping indicator.

Hope this helps.