Question

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

Answer 1

`(x-9)(x+2)`

Explanation:

The answer should be in the form
`(x+a)(x+b)=x^2 + (a+b)x + a*b`

So, in your equation you have
`a+b=-7`
and
`a*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*(-2)` or `(-9)*2` would both give -18.

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

There you have it! So, both `a*b` and `a+b` equations work when a=-9 and b=+2.
Putting those back in the first equation, we have:
`x^2 -7x -18 = (x-9)(x+2)`