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

Question

.(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 2 and x equals 4
x=−2
and x=−4

Answer 1

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

Setting each factor equal to zero:

1. \( x + 4 = 0 \)

   • Solving for \( x \) gives: \[ x = -4 \]

2. \( x - 2 = 0 \)

   • Solving for \( x \) gives: \[ x = 2 \]

Thus, the solutions to the equation are:

• \( x = -4 \)
• \( x = 2 \)

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