Question

Identify the factors of x2 − 4x − 12. (1 point)

(x + 4)(x − 3)

(x − 4)(x + 3)

(x − 2)(x + 6)

(x + 2)(x − 6)

Answer 1

x² - 4x - 12 =
x² + 2x - 6x - 12 =
x(x + 2) - 6(x + 2) =
(x + 2)(x - 6)

Answer 2

D.
`(x-6)(x+2)`

Explanation:

We have been given a polynomial
`x^2-4x-12`. We are asked to find the factors of our given polynomial.

We will use splitting the middle term format of factoring quadratic polynomial.

We need two numbers, whose product is
`-12` and whose sum is
`-4`. Such two numbers are
`-6\text{ and }2`.

`x^2-6x+2x-12`

`(x^2-6x)+(2x-12)`

Factor out GCF of each group:

`x(x-6)+2(x-6)`

`(x-6)(x+2)`

Therefore, factors of our given expression are
`(x-6)(x+2)` and option D is the correct choice.