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.