Question

Jedida solved the quadratic equation x^2−96=4x by factoring. Her work is shown below. At which step did Jedida first make a mistake, if at all? x^2−96=4x Step 1: x^2+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. 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. She did not make any mistakes.

Answer 1

Let's go through Jedida's work step by step to identify any mistakes:

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

2. **Step 1: Move all terms to one side**: Jedida rewrote the equation as \(x^2 + 4x - 96 = 0\). To do this correctly, she should have subtracted \(4x\) from both sides, resulting in \(x^2 - 4x - 96 = 0\). Therefore, she made a mistake in Step 1 by adding \(4x\) to both sides instead of subtracting it.

3. **Step 2: Factor**: After her initial mistake, Jedida factored the incorrectly rearranged equation as \((x + 12)(x - 8) = 0\). This is also incorrect because the correct factorization of \(x^2 - 4x - 96 = 0\) should involve different numbers (in fact, it should be \((x - 12)(x + 8) = 0\)). She made another mistake in this step, but it is rooted in her earlier mistake from Step 1.

4. **Step 3: Zero Product Property**: In her solution, she applied the zero product property correctly, but it was based on the incorrect factorization from before.

Considering these points, Jedida's first mistake occurred in **Step 1**, where she incorrectly added \(4x\) instead of subtracting it. Therefore, the response is:

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