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

1 Answer
Sep 20, 2015

Answer:

#(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)#