Question

Find the values of x that make the following equation equal zero: (x+4)(x−2)=0 .(1 point)
Responses

x=−4 and x=2
x equals negative 4 and x equals 2

x=−2 and x=4
x equals negative 2 and x equals 4

x=−2 and x=−4
x equals negative 2 and x equals negative 4

x=2 and x=4

Answer 1

To solve the equation \((x + 4)(x - 2) = 0\), we can use the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Set each factor equal to zero:

1. \(x + 4 = 0\)
- Solving for \(x\), we get \(x = -4\).

2. \(x - 2 = 0\)
- Solving for \(x\), we get \(x = 2\).

Therefore, the values of \(x\) that make the equation equal zero are \(x = -4\) and \(x = 2\).

The correct response is:
**x equals negative 4 and x equals 2**.