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

Question

(
𝑥
+
4
)
(
𝑥
−
2
)
=
0
(1 point)
Responses

x=2 and x=4
𝑥
=
2

𝑎
𝑛
𝑑

𝑥
=
4
x=2 and x=4
𝑥
=
2

Answer 1

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

Set 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 \((x + 4)(x - 2) = 0\) are:

\[ x = -4 \quad \text{and} \quad x = 2 \]

So the response should include both \(x = -4\) and \(x = 2\).