# How do you factor x^2+9x+18?

Apr 21, 2018

By finding what multiplies to give 18 and adds to give 9.

#### Explanation:

General form $a {x}^{2} + b x + c$
What does multiplies to give $a c$ and adds to give $b$

First is 18 positive or negative. If positive both factors will be positive or negative depending on the sign of $b$.
(Not this Question) If negative the factors will be opposite in sign.

List all the factors of $a c = 18$.
$1 , 18$
$2 , 9$
$3 , 6$
Now looking at these number intuitively what will add to give $b = 9$.

$3 , 6$

Now place into the form:
$\left(x + 6\right) \left(x + 3\right)$
This is the factorised version of ${x}^{2} + 9 x + 18$