Question

Hyung-eun is solving the quadratic equation x^2 - 4x - 12 = 0 by grouping. Her work is shown below. At which step does Hyung-eun first make an error?
Given equation: x^2 - 4x - 12 = 0

Step 1: x^2 + (-6x) + 2x - 12 = 0
Step 2: (x^2 + (-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

At which step does Hyung-eun first make an error?

A. Step 1
B. Step 2
C. Step 3
D. Step 4

Answer 1

To find where Hyung-eun first made an error, let's analyze each step of her work.

1. **Given Equation:** \( x^2 - 4x - 12 = 0 \)
2. **Step 1**: She rewrites the equation as \( x^2 + (-6x) + 2x - 12 = 0 \).
- Here, she incorrectly split \(-4x\) into \(-6x\) and \(2x\). The correct splits should have added up to -4. Thus, this step is incorrect.

Therefore, Hyung-eun first makes an error in **Step 1**.

The answer is **A. Step 1**.