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

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.

She did not make any mistakes.

Answer 1

Jedida's work can be evaluated step by step:

1. Step 1: \( x^2 - 96 = 4x \) She correctly moved \( 4x \) to the left side by adding \( 4x \) to both sides: \[ x^2 - 4x - 96 = 0 \] (Note: Here, it should have been \( x^2 - 4x - 96 = 0 \) instead of \( x^2 + 4x - 96 = 0 \).)

2. Step 2: She attempted to factor the equation: The equation should have been: \[ (x - 12)(x + 8) = 0 \] But she factored it as: \[ (x + 12)(x - 8) = 0 \] This is incorrect as the factors don't match the quadratic.

3. Step 3: She applies the Zero Product Property: Since the factors from Step 2 were incorrect, solving \( x + 12 = 0 \) and \( x - 8 = 0 \) would provide the wrong roots: \[ x = -12 \quad \text{or} \quad x = 8 \] This step is thus irrelevant due to the incorrect factorization.

Based on this analysis, the first mistake occurred in Step 1, where she incorrectly added \( 4x \), leading to the wrong quadratic to factor in Step 2.

So, the correct response is:

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