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

Sep 20, 2015

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

#### Explanation:

The answer should be in the form
$\left(x + a\right) \left(x + b\right) = {x}^{2} + \left(a + b\right) x + a \cdot b$

So, in your equation you have
$a + b = - 7$
and
$a \cdot b = - 18$
and we just need to solve for a and b.

Now, and this is very much intuitive, what easy multiplication do you know that give (-18) as an answer?
Yes, you got it.
$9 \cdot \left(- 2\right)$ or $\left(- 9\right) \cdot 2$ would both give -18.

What if you added them together?
$9 + \left(- 2\right) = 7$
whereas
$- 9 + 2 = - 7$
Surely, the second one is better for our equation.

There you have it! So, both $a \cdot b$ and $a + b$ equations work when a=-9 and b=+2.
Putting those back in the first equation, we have:
${x}^{2} - 7 x - 18 = \left(x - 9\right) \left(x + 2\right)$