Signs Under Pressure

To factor x^2 - x - 12, find two numbers whose product is -12 and whose sum is -1. They are -4 and 3, so x^2 - x - 12 = (x - 4)(x + 3). The equation becomes (x - 4)(x + 3) = 0.

Set each factor equal to zero: x = 4 or x = -3. Notice that the signs change twice. The pair inside the parentheses is -4 and 3. The solutions have the opposite signs, 4 and -3.

First check the signs in the factored form. Then solve each factor equation separately. x - 4 = 0 gives x = 4, and x + 3 = 0 gives x = -3.