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.

Answer 1

Jedida made a mistake in Step 1. The original equation is \( x^2 - 96 = 4x \). To properly rearrange the equation to set it to zero, she should subtract \( 4x \) from both sides, not add.

The correct step should have been:
\[ x^2 - 4x - 96 = 0. \]

Thus, the response "Step 1; she added 4x to both sides instead of subtracting." is correct.