Alexis,
A factor x-a by definition gives a function a root of a if dividing the function by x-a gives a remainder of 0. That means dividing by x+2 should give a remainder of 0. If x-2 is a factor, it should also give a remainder of 0 when you divide the function by it.
Since the first term is x^3, we know there are three possible roots. Not all of them may be rational though! You'll just have to keep dividing until you get something prime.
So in this case, we already know -2 is a root so dividing the function by x+2 gives us:
x^2+5x-6
You can use whatever method at this point to find the two remaining roots which will be integers.
