Answer:
Option D, (x - 7)(x + 6)
Step-by-step explanation:
With quadratic expressions in the form ax² + bx + c, the first step in the process is finding factors for the product of coefficient a and constant c with a sum that equals coefficient b.
For the expression x² - x - 42,
a = 1
b = -1
c = -42
Now, we list factor pairs of -42 has a sum of -1:
-1, 42; -2, 21; -3, 14; -6, 7; 1, -42; 2, -21; 3, -14; 6, -7
The last factor pair has a sum of -1, therefore we substitute these values as coefficients b, separate terms into binomials, and factor out the greatest common factors (GCF) of each binomial:
x² + 6x - 7x - 42
(x² + 6x) + (-7x - 42)
The GCF of x² and 6x is x. The GCF of -7x and -42 is -7.
x(x + 6) - 7(x + 6)
The binomial inside each set of parentheses matches, so we have found our factors. They are the binomial within the parentheses and the GCFs on the outside:
(x + 6)(x - 7)
This aligns with option D.