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 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.
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Answer 1

To analyze Jedida's solution, let's go through her steps systematically:

1. Start with the given equation: \[ x^2 - 96 = 4x \]

2. Rearrange the equation:

   • Correctly, to set it to zero, you should subtract \(4x\) from both sides, not add: \[ x^2 - 4x - 96 = 0 \] So, Step 1 is where Jedida first made a mistake.

3. Step 2 shows her factoring it as: \[ (x + 12)(x - 8) = 0 \] This is incorrect based on the previous mistake.

4. Step 3 applies the Zero Product Property based on the incorrect factorization.

In conclusion, the first mistake occurs in Step 1, where she added \(4x\) to both sides instead of subtracting it. Thus, the correct answer is:

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