Jedida solved the quadratic equation x^2−96=4x

Question

by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all?

x^2−96=4x
Step 1: x^2+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 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.

She did not make any mistakes.
She did not make any mistakes.

Step 1; she added 4x
to both sides instead of subtracting.
Step 1; she added 4 x to both sides instead of subtracting.

Step 3; she did not apply the Zero Product Property correctly.

Answer 1

Jedida made a mistake in Step 2. The quadratic equation she started with was \( x^2 - 96 = 4x \). After moving \( 4x \) to the left side correctly in Step 1, she should have obtained:

\[ x^2 - 4x - 96 = 0 \]

In Step 2, she incorrectly factored \( x^2 - 4x - 96 \) as \( (x + 12)(x - 8) \). The correct factorization should be \( (x - 12)(x + 8) \), hence the statement "Step 2; she did not factor the left side of the equation correctly" is accurate.

So the correct response is:

Step 2; she did not factor the left side of the equation correctly.