Jedida solved the quadratic equation x^2−96=4x

Question

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 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 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 3; she did not apply the Zero Product Property correctly.

Answer 1

Let's look at Jedida's steps to determine if there were any mistakes.

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

   Step 1: To rewrite the equation in standard form, Jedida adds \(4x\) to both sides:

   \[ x^2 - 96 - 4x = 0 \implies x^2 + 4x - 96 = 0 \]

   This step is correct.

2. Step 2: She factors \(x^2 + 4x - 96\) and states:

   \[ (x + 12)(x - 8) = 0 \]

   To confirm this factorization, we can check: \( (x + 12)(x - 8) = x^2 - 8x + 12x - 96 = x^2 + 4x - 96 \).

   This is correct as well.

3. Step 3: Using the Zero Product Property, she sets each factor equal to zero:

   \[ x + 12 = 0 \quad \text{or} \quad x - 8 = 0 \]

   Solving these gives \( x = -12 \) or \( x = 8 \), both of which are also correct.

Since every step she took is correct, the conclusion is:

She did not make any mistakes.