What are the factors of x² − 13x + 42?

Correct answer: (x − 6)(x − 7)

The direct answer is A: (x − 6)(x − 7). For a monic quadratic x² + bx + c, find two numbers whose product is c and whose sum is b. Here, the product must be 42 and the sum must be −13. The numbers −6 and −7 satisfy both conditions: (−6)(−7) = 42 and −6 + (−7) = −13. Therefore x² − 13x + 42 = (x − 6)(x − 7). Option A is correct because expansion gives x² − 7x − 6x + 42 = x² − 13x + 42. Option B gives a positive middle term, x² + 13x + 42, so its signs are wrong. Option C gives factors with sum −17, producing x² − 17x + 42. Option D gives factors with sum −43, producing x² − 43x + 42. Memory cue: when the constant is positive and the middle coefficient is negative, both factor numbers are usually negative.