Question

Which of the following values are zeros for the function below? Select all that apply.
g (x) = (x^2 + 4x - 12)(x - 3)

Answer 1

Zeros occur when the function evaluates to 0.

To find the zeros of the function g(x), we set g(x) equal to 0 and solve for x:

0 = (x^2 + 4x - 12)(x - 3)

The zeros occur at the values of x that make the function equal to zero.

1. Set the expression inside the parentheses equal to 0:

x^2 + 4x - 12 = 0
(x + 6)(x - 2) = 0

Using the zero-product property, we can find the zeros:

x + 6 = 0 → x = -6
x - 2 = 0 → x = 2

2. Set the other expression inside the parentheses equal to 0:

x - 3 = 0
x = 3

Therefore, the zeros of the function g(x) are x = -6, x = 2, and x = 3.