Both Negative

Positive constant, negative middle: x^2 - 7x + 12. The product +12 says SAME signs; the sum -7 says both are negative. The hunt is the familiar one through pairs of 12, all in minus: -3 and -4.

Check: (-3)(-4) = 12 and -3 - 4 = -7. So x^2 - 7x + 12 = (x - 3)(x - 4): two minus parentheses, and the expansion's cross products rebuild the negative middle while the lasts multiply back to plus.

This case trips the eye because the constant looks innocent. Read BOTH signs before hunting: plus c with minus b is the both-negative cell of the map, and every pair candidate wears a minus.