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

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

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

Answer 1

Let's analyze Jedida's steps to identify if she made any mistakes.

1. Original equation: \( x^2 - 96 = 4x \)

2. Step 1: \( x^2 - 96 = 4x \) She adds \( 4x \) to both sides: \[ x^2 + 4x - 96 = 0 \] This step is correct.

3. Step 2: She factors the left side: \( (x + 12)(x - 8) = 0 \) To verify this, let's expand \( (x + 12)(x - 8) \): \[ x^2 - 8x + 12x - 96 = x^2 + 4x - 96 \] This is correct.

4. Step 3: She applies the Zero Product Property: \[ x + 12 = 0 \quad \text{or} \quad x - 8 = 0 \] From this, she concludes: \[ x = -12 \quad \text{or} \quad x = 8 \] This applies the Zero Product Property correctly.

Since all of her steps were correct, including her factoring, she did not make any mistakes.

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