How do I factor this quadratic expression as the product of two binomials

x^2-x-42

(x + 6) (x - 7)

Step-by-step explanation:

Look for factors of - 42 (the constant) that have a sum of - 1 (the x coefficient).

-42 = 1*-42 = 2*-21 = 3*-14 = 6*-7

Sums of these factor pairs are - 41, - 19, - 11, and - 1. The last two factors are the ones that are the constants in your binomial terms:

x^2 - x - 42 = (x + 6) (x - 7)