Jedida solved the quadratic equation x2−96=4x
by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?
x2−96=4x
Step 1: x2+4x−96=0
Add 4x
to both sides.
Step 2: (x+12)(x−8)=0
Factor.
Step 3: x+12=0
or x−8=0
Use the Zero Product Property.
x=−12
or x=8
(1 point)
Responses
Step 3; she did not apply the Zero Product Property correctly.
Step 3; she did not apply the Zero Product Property correctly.
She did not make any mistakes.
She did not make any mistakes.
Step 2; she did not factor the left side of the equation correctly.
Step 2; she did not factor the left side of the equation correctly.
Step 1; she added 4x
to both sides instead of subtracting.
Step 1; she added 4x to both sides instead of subtracting.
Step 2; she did not factor the left side of the equation correctly.
Step 3: she did not apply the Zero Product Property correctly.
To solve the quadratic equation x^2 - 96 = 4x by factoring, Jedida correctly rearranged the equation in Step 1 to get x^2 + 4x - 96 = 0. Then in Step 2, she factored the left side of the equation correctly as (x + 12)(x - 8) = 0.
The mistake occurred in Step 3 when Jedida applied the Zero Product Property. The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore, to solve the equation, each factor should be set equal to zero.
Instead, Jedida only set one factor equal to zero, which led to the incorrect solutions x = -12 and x = 8. The correct solutions should be x = -12 or x = 8.