Convert q² + q − 56 into factors.

Correct answer: (q + 8)(q − 7)

The direct answer is A: (q + 8)(q − 7). For a quadratic of the form q² + bq + c, look for two numbers whose product is c and whose sum is b. Here the product must be −56 and the sum must be 1. The numbers 8 and −7 satisfy both conditions: 8 × (−7) = −56 and 8 + (−7) = 1. Hence q² + q − 56 = q² + 8q − 7q − 56. Grouping gives q(q + 8) − 7(q + 8) = (q + 8)(q − 7). Option A is therefore correct. Option B uses −8 and +7; their product is −56, but their sum is −1, so it would produce q² − q − 56. Option C uses 4 and −14; their product is −56, but their sum is −10. Option D uses −1 and 56; their product is −56, but their sum is 55. The safest check is to multiply the two proposed binomials and compare both the middle coefficient and the constant term. Memory cue: product gives the last term; sum gives the coefficient of the middle term.