Hyung-eun is solving the quadratic equation x2−4x−12=0 by grouping. Her work is shown below. At which step does Hyung-eun first make an error?

Question

x2−4x−12=0

Step1: x2+(−6x)+2x−12=0

Step 2: (x2+(−6x))+(2x−12)=0

Step 3: x(x+(−6))+2(x−6)=0

x(x−6)+2(x−6)=0

Step 4: (x+6)(x−2)=0

Step 5: x+6=0 or x−2=0

x=−6 or x=2

(1 point)
Responses

Step 3
Step 3

Step 1
Step 1

Step 2
Step 2

Step 4

Answer 1

Hyung-eun makes an error in Step 1.

Let's analyze each step:

1. In the equation \( x^2 - 4x - 12 = 0 \), when she rewrites it as \( x^2 + (-6x) + 2x - 12 = 0 \), she incorrectly factors the middle term, as \( -6x + 2x \) does not equal \( -4x \).

Thus, the mistake occurs in Step 1.