Question

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

x=−2
and x=4
x is equal to negative 2 and x is equal to 4

x=2
and x=4
x is equal to 2 and x is equal to 4

x=−4
and x=2
x is equal to negative 4 and x is equal to 2

x=−2
and x=−4

Answer 1

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

Setting each factor equal to zero gives us:

1. \(x + 4 = 0\)
- Solving for \(x\) gives \(x = -4\).

2. \(x - 2 = 0\)
- Solving for \(x\) gives \(x = 2\).

Thus, the values of \(x\) that make the equation equal zero are:
- \(x = -4\)
- \(x = 2\)

The correct response is:
**x=−4 and x=2 (x is equal to negative 4 and x is equal to 2).**