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 \( 8x^4 - 6x^2 - 5x \).