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

Question

.(1 point)
Responses

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

x=2
and x=4
x equals 2 and x equals 4

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

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

Answer 1

To find the values of \( x \) that make the equation \( (x+4)(x-2) = 0 \) equal to zero, we can use the property that if the product of two factors is zero, then at least one of the factors must be zero.

Setting each factor equal to zero gives:

1. \( x + 4 = 0 \)
2. \( x - 2 = 0 \)

Solving these equations:

1. From \( x + 4 = 0 \): \[ x = -4 \]

2. From \( x - 2 = 0 \): \[ x = 2 \]

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

Therefore, the correct response is:

x=−4 and x=2 (x equals negative 4 and x equals 2).