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 equals negative 2 and x equals negative 4 x=−2 and x=4 x equals negative 2 and x equals 4 x=−4 and x=2 x equals negative 4 and x equals 2 x=2 and x=4
The correct responses are:
- x = -4 and x = 2
To solve the equation (x + 4)(x - 2) = 0, we need to find the values of x that make the equation equal to zero.
The equation is set to zero when either (x + 4) = 0 or (x - 2) = 0.
Let's solve each equation separately:
1. To find the value of x when (x + 4) = 0, we subtract 4 from both sides: x + 4 - 4 = 0 - 4, which simplifies to x = -4.
2. To find the value of x when (x - 2) = 0, we add 2 to both sides: x - 2 + 2 = 0 + 2, which simplifies to x = 2.
Therefore, the values of x that make the equation (x + 4)(x - 2) = 0 equal to zero are x = -4 and x = 2.
So, the correct response is: x = -4 and x = 2.
To find the values of x that make the equation equal to zero, we need to set each factor equal to zero and solve for x.
(x + 4)(x - 2) = 0
Setting the first factor equal to zero:
x + 4 = 0
x = -4
Setting the second factor equal to zero:
x - 2 = 0
x = 2
Therefore, the values of x that make the equation equal zero are x = -4 and x = 2.