In which form will x² − 13x + 42 be written?

Correct answer: (x − 6)(x − 7)

Correct answer: A, (x − 6)(x − 7). To factor x² − 13x + 42, find two numbers whose product is 42 and whose sum is −13. The numbers are −6 and −7 because (−6)(−7) = 42 and −6 + −7 = −13. Therefore x² − 13x + 42 = (x − 6)(x − 7). Checking by multiplication gives x² − 7x − 6x + 42 = x² − 13x + 42. Option A is correct because both required conditions match. Option B gives x² + 13x + 42, so its middle sign is wrong. Option C gives x² − 17x + 42, so the middle coefficient is wrong. Option D gives x² − 11x − 42, so both the middle and constant terms do not match. Memory cue: for a positive last term and a negative middle term, both factor numbers are negative.