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: $$x=-12\text{or}x=8$$ 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.