Jedida solved the quadratic equation x? - 96 = 4x by factoring. Her
work is shown below. At which step did Jedida first make a mistake, if at all?
x? - 96 = 4х
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)
• Step 3; she did not apply the Zero Product Property correctly.
• Step 1; she added 4x to both sides instead of subtracting.
• Step 2; she did not factor the left side of the equation correctly.
• She did not make any mistakes.
page 1 of 1
Step 3; she did not apply the Zero Product Property correctly.
Jedida did not make any mistakes in solving the quadratic equation x² - 96 = 4x.
In this scenario, Jedida is trying to solve the quadratic equation x^2 - 96 = 4x by factoring. Let's examine each step to identify any potential mistakes.
Step 1: Jedida rewrote the equation as x^2 + 4x - 96 = 0. This step involves rearranging the terms and bringing all the terms to one side of the equation, which Jedida has done correctly. Therefore, there is no mistake in this step.
Step 2: Jedida factored the left side of the equation as (x + 12)(x - 8) = 0. This is the correct factorization of the quadratic equation, breaking it down into two binomials. Hence, there is no mistake in this step.
Step 3: Jedida applied the Zero Product Property correctly by setting each factor equal to zero and solving for x. This is the correct approach in factoring since if the product of two factors equals zero, then at least one of the factors must be zero. Therefore, there is no mistake in this step.
Based on the analysis of each step, it appears that Jedida did not make any mistakes. The correct answer is: "She did not make any mistakes."