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A student subtracted two polynomials. They asked a friend to check their solution and work. What should their friend tell them? Are they correct? If they are not correct, in which step did the student make an error? (3x4−8x2+4x)−(9x−5x4+2x2)(3x4−8x2+4x)−(9x−5x4+2x2) Step 1: 3x4−8x2+4x−9x+5x4+2x23x4−8x2+4x−9x+5x4+2x2 Step 2: 3x4+5x4−8x2+2x2+4x−9x3x4+5x4−8x2+2x2+4x−9x Step 3: 8x4−6x2−5x8x4−6x2−5x Final Answer: 8x4−6x2−5x8x4−6x2−5x(1 point) Responses The student is correct The student is correct - no response given The student is incorrect The student is incorrect - correct Check Answer Question 2 If the student is incorrect, explain in which step the student made an error AND what the error was?(2 points)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
1 month ago

The student is **incorrect** in their polynomial subtraction work, and the error occurs in **Step 2**.

### Breakdown of the Steps:

1. **Step 1**: The student correctly rewrites the subtraction of the second polynomial as adding the opposite of each term from the second polynomial, transforming the expression into:
\[
3x^4 - 8x^2 + 4x - 9x + 5x^4 + 2x^2
\]

2. **Step 2**: Here, the student appears to correctly regroup the terms, but they make a mistake in combining the coefficients of the terms:
- For the \( x^4 \) terms:
\[
3x^4 + 5x^4 = 8x^4
\]
- For the \( x^2 \) terms:
\[
-8x^2 + 2x^2 = -6x^2
\]
- For the \( x \) terms:
\[
4x - 9x = -5x
\]

However, on reviewing the text presented, the student neglects to address \( -9x \) properly in their summary.

3. **Step 3**: In the final answer, the terms should have included \( -5x \) but they omitted it:
\[
8x^4 - 6x^2 - 5x
\]

### Conclusion:
The final answer the student wrote down lacks the \( -5x \) term, leading to the misunderstanding. Thus, the final correct expression should be:
\[
8x^4 - 6x^2 - 5x
\]

### Answer to Question 2:
The student is incorrect. The error occurred in Step 2, where they failed to combine the \( x \) terms correctly. They missed retaining the term \( -5x \) in their final answer. The correctly simplified expression should be \( 8x^4 - 6x^2 - 5x \).