Let's verify the steps to see if the student performed the subtraction correctly.
Given polynomials:
\[
(3x^4−8x^2+4x)−(9x−5x^4+2x^2)
\]
**Step 1:** Rewrite the expression correctly.
\[
3x^4 - 8x^2 + 4x - (9x - 5x^4 + 2x^2)
\]
Distributing the negative sign (subtracting the whole second polynomial):
\[
3x^4 - 8x^2 + 4x - 9x + 5x^4 - 2x^2
\]
The expression should be:
\[
3x^4 + 5x^4 - 8x^2 - 2x^2 + 4x - 9x
\]
**Step 2:** Combine like terms.
1. Combine \(3x^4\) and \(5x^4\):
\[
3x^4 + 5x^4 = 8x^4
\]
2. Combine \(-8x^2\) and \(-2x^2\):
\[
-8x^2 - 2x^2 = -10x^2
\]
3. Combine \(4x\) and \(-9x\):
\[
4x - 9x = -5x
\]
Putting it all together, we have:
\[
8x^4 - 10x^2 - 5x
\]
**Verification of the student's final answer:**
The student's final answer was \(8x^4 - 6x^2 - 5x\). The correct answer after correctly processing the subtraction is \(8x^4 - 10x^2 - 5x\).
**Conclusion:**
The student made an error in Step 2 when adding \(-8x^2\) and \(2x^2\). The correct result should have been \(-10x^2\), not \(-6x^2\). Therefore, their friend should tell them that they made an error in combining like terms, specifically with the \(x^2\) terms, and the final answer is not correct. The correct answer is \(8x^4 - 10x^2 - 5x\).