In a rectangle model, the small corner area is (-30) and the sum of middle strips is (x). For (x^2+x-30), which sides are correct?

Correct answer: (x+6) and (x-5) / signed sides

The correct answer is A: (x+6)(x-5). To factor x^2+x-30, find two numbers whose product is -30 and whose sum is +1, because the middle coefficient is +1. The numbers are +6 and -5: 6 times -5=-30 and 6+(-5)=1. Therefore x^2+x-30=(x+6)(x-5). In a rectangle model, the x^2 tile supplies the variable parts, the signed corner tiles multiply to -30, and the two middle strips combine to +x. Option A satisfies both checks. Option B also has product -30, but its constants add to -1, giving x^2-x-30, so its middle sign is wrong. Option C has constants with product -30 but sum 7, giving x^2+7x-30. Option D has product -30 but sum -29, not +1. Memory cue: for a monic quadratic, check both the product of constants and their sum before accepting the factorisation.