Question

What is the factored form of the following expression?

x^2 - x - 42

Answer 1

Factor x²−x−42 using the AC method.

(x+6)(x-7)

Explanation:

What is the factored form of the following expression?

x^2 - x - 42

STEPS:

x²-x-42

Break the expression into groups:

=(x²+6x)+(-7x-42)

Factor out x from x²+6x: x(x+6)

Factor out -7 from -7-42: -7(x+6)

=x(x+6)-7(x+6)

Factor out common term x+6

ANSWER=(x+6)(x-7)

Answer 2

(x - 7)(x + 6)

Explanation:

Consider the factors of the constant term ( - 42) which sum to give the coefficient of the x- term ( - 1)

The factors are - 7 and + 6, since

- 7 × 6 = - 42 and - 7 + 6 = - 1

x² - x - 42 = (x - 7)(x + 6)