I seem to be having a problem when factoring this. Though I already know what the answer is, I'm confused on how that answer is actually gotten.

Equation: x^2-2x-2

First, I try finding a product sum answer that will fullfill the requirments - when multiplied together equal -2 and when added together equal -2.

And this is where the problem sets in. The only possible number combination is 2 and 1, because they need to equal 2 when multiplied together. But there is no way to do this without having their sum be -3, -1, 1, or 3.

This is just made more complicated by the fact that the factor is (x-3)(x+1), or at least that's what I figure from the graph since it has zeroes of 3 and -1.

Any idea what I could be doing wrong here?