The student is incorrect in their polynomial subtraction work, and the error occurs in Step 2.
Breakdown of the Steps:
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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: \[ 3x^4 - 8x^2 + 4x - 9x + 5x^4 + 2x^2 \]
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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.
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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 \( 8x^4 - 6x^2 - 5x \).
2 answers