Asked by ,


Solving Quadratic Equations Using Common Factors Quick Check
4 of 54 of 5 Items
Question
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?

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 2
Step 2

Step 4
Step 4

Step 3
Step 3

Step 1
Step 1
Skip to navigation
page 16 of 16
Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answers

Answered by GPT-4o mini
To identify the error in Hyung-eun's steps when solving the quadratic equation \(x^2 - 4x - 12 = 0\) by grouping, we can analyze each step:

1. **Original Equation**: \(x^2 - 4x - 12 = 0\)

2. **Step 1**: \(x^2 + (-6x) + 2x - 12 = 0\)
- This step factors the middle term incorrectly. The correct grouping should lead to two numbers that multiply to \(-12\) and add up to \(-4\). The numbers are \(-6\) and \(2\), but they should combine to be \(x^2 - 6x + 2x - 12\).

3. **Step 2**: \((x^2 + (-6x)) + (2x - 12) = 0\)
- This step is simply regrouping the previous expression, so it is still fine.

4. **Step 3**: \(x(x + (-6)) + 2(x - 6) = 0\)
- This also seems to be a correct grouping step.

5. **Step 4**: \((x + 6)(x - 2) = 0\)
- This step is where the significant error occurs because the product should not match the factors derived from the earlier steps. The correct factorization should have been \((x - 6)(x + 2)\).

6. **Step 5**: Solving for the roots based on an incorrect factorization leads to incorrect solutions.

Given this analysis, the first error occurs in **Step 1**, where she incorrectly breaks down the middle term into \((-6x)\) and \(2x\). Therefore, the correct answer is:

**Step 1 - She incorrectly grouped the terms.**
There are no human answers yet. A form for humans to post answers is coming very soon!

Related Questions