Which One Gets the Minus

With opposite signs, the sum is really a difference, and its SIGN follows the larger number. x^2 - 2x - 15: product -15, sum -2. The pair 5 and 3 differ by 2, and the sum must be negative, so the larger one takes the minus: -5 and 3.

Check: (-5) * 3 = -15 and -5 + 3 = -2. So x^2 - 2x - 15 = (x - 5)(x + 3).

The working recipe for negative c: hunt pairs whose DIFFERENCE is the middle's size, then hang the minus on the larger number if the middle is negative, on the smaller if positive. Two decisions, both read straight off the signs.