Both Negative

Now the constant is positive and the middle coefficient is negative, as in x^2 - 7x + 12. The product +12 is positive, so the two numbers have the same sign. The sum -7 is negative, so both numbers are negative. List the factor pairs of 12 as before, and make both numbers negative. The pair is -3 and -4.

Check: (-3)(-4) = 12 and -3 - 4 = -7. So x^2 - 7x + 12 = (x - 3)(x - 4). Both factors have a minus sign. When you expand, the two cross products add to the negative middle term, and the two negative last terms multiply to the positive constant.

Look at both the constant and the middle coefficient. A positive constant means the two numbers have the same sign. If the middle coefficient is also negative, both numbers are negative.