# Thread: Partial Fraction Decomposition

1. ## Partial Fraction Decomposition

Hi everyone!
I need a helping hand here with factoring this denominator:

$\frac {-5x + 15}{x^2 + 2x - 63}$

I feel a bit stupid, can I use completing the square? Or do I need to use the quadratic formula? If I complete the square I think I got...

$(x-1)^2 - 64$

I don't know, rather confused.

2. ## Response

Remember how to factor something like $x^2-5x+6$?
Remember the middle term (-5x) is the sum of the product of the coefficient of the first and last term. So in this case the only numbers that would add up to -5 (coefficient of middle term) and whose product would be +6 would be -3 and -2. So from here, you could expand the expression as $x^2-3x-2x+6 -> x(x-3)-2(x-3)= (x-2)(x-3)$
There should be a common factor in both pars (x-3). I do not want to give you the answer (sorry!). Hopefully, this will trigger your memory.

3. Hohoho, I'm so bad at basic math.
Yeah you're right, so it's...

$(x+9) (x-7)$
Thank you!
bahahah....