You find 2 numbers with a difference or sum of 2 which multiply to give -8.
One possibility is that the numbers are -4 and 2, but the sign of the 2x term is needed. If the full equation is x2 - 2x - 8 then the factors are (x - 4)(x + 2)
On the other hand if the 2x term is positive the factors are (x + 4)(x - 2)
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x2 + 2x - 48 = x2 + 8x - 6x - 48 = x(x + 8) - 6(x + 8) = (x - 6)(x + 8)
x3 + 8 = x3 + 23 = (x + 2)(x2 + 2x + 22) = (x + 2)(x2 + 2x + 4)
x2 + 2x - 15 = (x + 5)(x - 3)
(2x3 - x2) = x2 (2x - 1)
-x2 + 2x + 48 = (-x - 6)(x - 8) = -(x + 6)(x - 8)