Question

What are the factors of x^2 - x - 6? Check all that apply.

Factor 1:
a) x²
b) x - 6
c) x + 6
d) mx - 3

Factor 2:
a) x + 2
b) x + 1
c) x - 1
d) mx - 2

Answer 1

Factor 1: b) x - 6 and c) x + 6 are factors of x² - x - 6.

Factor 2: b) x + 1 and c) x - 1 are factors of x² - x - 6.

Step-by-step explanation:

To determine the factors of x² - x - 6, we search for two binomials whose product equals the given quadratic expression. We need pairs of numbers that multiply to the product of the leading coefficient (1) and the constant term (-6) and add up to the coefficient of the linear term (-1).

For Factor 1, the pair of numbers is 3 and -2 because (x - 2) * (x + 3) gives x² - x - 6. Therefore, b) x - 6 and c) x + 6 are factors.

For Factor 2, the pair of numbers is 2 and -3 because (x + 2) * (x - 3) gives x² - x - 6. Therefore, b) x + 1 and c) x - 1 are factors.

It's crucial to note that the options with mx - 3 and mx - 2 are not factors of x² - x - 6 since the correct pairs of factors are those that directly multiply to give the quadratic expression. Therefore, the final answer consists of the correct factorization pairs, as indicated above.