Question

Caleb's work to find the difference (−4.6k2+2.5k−3.8)−(3.6k+5.1k2)%0D%0A(%0D%0A−%0D%0A4.6%0D%0A%0D%0A2%0D%0A+%0D%0A2.5%0D%0A%0D%0A−%0D%0A3.8%0D%0A)%0D%0A−%0D%0A(%0D%0A3.6%0D%0A%0D%0A+%0D%0A5.1%0D%0A%0D%0A2%0D%0A)%0D%0AGiven: (−4.6k2+2.5k−3.8)−(3.6k+5.1k2)%0D%0A(%0D%0A−%0D%0A4.6%0D%0A%0D%0A2%0D%0A+%0D%0A2.5%0D%0A%0D%0A−%0D%0A3.8%0D%0A)%0D%0A−%0D%0A(%0D%0A3.6%0D%0A%0D%0A+%0D%0A5.1%0D%0A%0D%0A2%0D%0A)%0D%0AStep 1: −4.6k2+2.5k−3.8−3.6k+5.1k2%0D%0A−%0D%0A4.6%0D%0A%0D%0A2%0D%0A+%0D%0A2.5%0D%0A%0D%0A−%0D%0A3.8%0D%0A−%0D%0A3.6%0D%0A%0D%0A+%0D%0A5.1%0D%0A%0D%0A2%0D%0AStep 2: −4.6k2+5.1k2+2.5k−3.6k−3.8%0D%0A−%0D%0A4.6%0D%0A%0D%0A2%0D%0A+%0D%0A5.1%0D%0A%0D%0A2%0D%0A+%0D%0A2.5%0D%0A%0D%0A−%0D%0A3.6%0D%0A%0D%0A−%0D%0A3.8%0D%0AStep 3: 0.5k2−1.1k−3.8%0D%0A0.5%0D%0A%0D%0A2%0D%0A−%0D%0A1.1%0D%0A%0D%0A−%0D%0A3.8%0D%0AComplete the statements. %0D%0A%0D%0A(2 points)%0D%0APut responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.%0D%0ACaleb Response area.%0D%0A%0D%0AThe difference of (−4.6k2+2.5k−3.8)−(3.6k+5.1k2)%0D%0A(%0D%0A−%0D%0A4.6%0D%0A%0D%0A2%0D%0A+%0D%0A2.5%0D%0A%0D%0A−%0D%0A3.8%0D%0A)%0D%0A−%0D%0A(%0D%0A3.6%0D%0A%0D%0A+%0D%0A5.1%0D%0A%0D%0A2%0D%0A)%0D%0A is Response area %0D%0A%0D%0Acorrectly found the difference of the polynomialsfirst made a mistake in Step 1first made a mistake in Step 2first made a mistake in Step 30.5k2−1.1k−3.8%0D%0A0.5%0D%0A%0D%0A2%0D%0A−%0D%0A1.1%0D%0A%0D%0A−%0D%0A3.8%0D%0A0.5k2−1.1k+3.8%0D%0A0.5%0D%0A%0D%0A2%0D%0A−%0D%0A1.1%0D%0A%0D%0A+%0D%0A3.8%0D%0A−9.7k2+1.1k+3.8%0D%0A−%0D%0A9.7%0D%0A%0D%0A2%0D%0A+%0D%0A1.1%0D%0A%0D%0A+%0D%0A3.8%0D%0A−9.7k2−1.1k−3.8%0D%0A−%0D%0A9.7%0D%0A%0D%0A2%0D%0A−%0D%0A1.1%0D%0A%0D%0A−%0D%0A3.8

Answer 1

To determine whether Caleb correctly found the difference of the polynomials in his steps, let's analyze the expressions step by step and check for mistakes.

1. **Original Expression**:
\[
(−4.6k^2 + 2.5k − 3.8) − (3.6k + 5.1k^2)
\]

2. **Step 1**: Distributing the negative sign:
\[
-4.6k^2 + 2.5k - 3.8 - 3.6k - 5.1k^2
\]

3. **Step 2**: Combining like terms:
- For \(k^2\) terms:
\(-4.6k^2 - 5.1k^2 = -4.6 - 5.1 = -9.7k^2\)

- For \(k\) terms:
\(2.5k - 3.6k = 2.5 - 3.6 = -1.1k\)

- Constant term:
\(-3.8\) (remains the same)

Putting these together, we have:
\[
-9.7k^2 - 1.1k - 3.8
\]

4. **Now let's summarize what Caleb wrote**:
From Caleb's Step 3, he concluded:
\[
0.5k^2 - 1.1k - 3.8
\]
which is incorrect. The correct result after combining the like terms should be:
\[
-9.7k^2 - 1.1k - 3.8
\]

Based on this analysis, we can determine Caleb's mistakes:

- **Response Area Fill-In**:
Caleb **first made a mistake in Step 2**.

Now to answer the whole statement:
The difference of \((−4.6k^2 + 2.5k − 3.8) − (3.6k + 5.1k^2)\) is:
\(-9.7k^2 - 1.1k - 3.8\) (not as Caleb found it).
This means he correctly found the difference of the polynomials **but made a mistake in Step 2**.

In conclusion, Caleb's calculation needs correction primarily **in Step 2**.