Question

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

Answer 1

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

Explanation:

General form `ax^2+bx+c`
What does multiplies to give `ac` 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 `ac = 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:
`(x+6)(x+3)`
This is the factorised version of `x^2+9x+18`

Quadratic Equation also works.