Question

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

x to the second power −4x−12=0

Step1: x to the second power +(−6x)+2x−12=0

Step 2: (x to the second power +(−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 4
Step 4

Step 1
Step 1

Step 3
Step 3

Step 2
Step 2
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Answer 1

the answer

Answer 2

To identify where Hyung-eun first makes an error, let's review her steps carefully:

The original equation is:

\[ x^2 - 4x - 12 = 0 \]

**Step 1:**
\[ x^2 + (-6x) + 2x - 12 = 0 \]

This step is incorrect. The terms \(-6x\) and \(2x\) do not properly combine to give the middle term \(-4x\). The correct grouping should have simplified to:

\[ x^2 - 6x + 2x - 12 = 0 \]
which can be rearranged correctly to combine to \(x^2 - 4x - 12 = 0\).

**Step 2:**
In her step, she attempts to factor the expression. This is based on her incorrect step 1.

**Step 3:**
She factors the incorrect grouping, which is also wrong since it stems from the error in step 1.

**Step 4:**
Here, she writes out the factors based on incorrect grouping, also stemming from errors in the prior steps.

The first clear error occurs in **Step 1** because she incorrectly rearranged the equation's quadratic coefficients, leading to all subsequent errors. Therefore, the correct answer is:

**Step 1**.

Answer 3

The answer is **Step 1**.