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.

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 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.

Answer 1

To determine if Jedida made a mistake in solving the quadratic equation \( x^2 - 96 = 4x \), let's analyze her steps:

1. Step 1: \( x^2 - 96 = 4x \)
   She rewrites the equation to \( x^2 + 4x - 96 = 0 \) by adding \( 4x \) to both sides. This step is correct because she correctly moved \( 4x \) to the left side of the equation.

2. Step 2: \( (x+12)(x-8) = 0 \)
   Next, she factors \( x^2 + 4x - 96 \). The correct factorization should yield \( (x+12)(x-8) = 0 \) since: \[ (x + 12)(x - 8) = x^2 - 8x + 12x - 96 = x^2 + 4x - 96 \] Therefore, this step is also correct.

3. Step 3: \( x + 12 = 0 \) or \( x - 8 = 0 \)
   Applying the Zero Product Property is correct here, as she finds the roots from \( (x+12)(x-8) = 0 \).

Since all steps are performed correctly: She correctly moved \( 4x \) to one side, accurately factored the quadratic, and correctly applied the Zero Product Property.

Thus, the answer is: She did not make any mistakes.