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?

Question

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

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

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

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

Answer 1

Jedida made a mistake in Step 1. The correct process for solving the quadratic equation \( x^2 - 96 = 4x \) requires moving all terms to one side of the equation. Specifically, she should have subtracted \( 4x \) from both sides, not added it.

Therefore, the correct equation after Step 1 should be:

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

Because of this mistake, her factoring in Step 2 is also incorrect.

So the correct response is: Step 1; she added 4x to both sides instead of subtracting.