Question

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?

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.**