Which is the correct factorisation 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 their product must be 42 and their sum must be −13. The numbers −6 and −7 work because (−6)(−7) = 42 and −6 + (−7) = −13. Hence x² − 13x + 42 = (x − 6)(x − 7). Option B gives a positive middle term, x² + 13x + 42. Option C uses −3 and −14, whose sum is −17, not −13. Option D uses −2 and −21, whose sum is −23. Memory cue: when the constant is positive and the middle coefficient is negative, both factor signs are often negative; confirm by sum and product.