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+2𝑥2Step 2: 3x4+5x4−8x2+2x2+4x−9x3𝑥4+5𝑥4−8𝑥2+2𝑥2+4𝑥−9𝑥Step 3: 8x4−6x2−5x8𝑥4−6𝑥2−5𝑥Final Answer: 8x4−6x2−5x

To check the student's work, we need to look at each step of their polynomial subtraction and see if they have performed it correctly.

The original expression to simplify is:
\[
(3x^4 - 8x^2 + 4x) - (9x - 5x^4 + 2x^2)
\]

### Step 1:
The student rewrote the expression as:
\[
3x^4 - 8x^2 + 4x - 9x + 5x^4 + 2x^2
\]
This step is correct. They correctly distributed the negative sign across the second polynomial.

### Step 2:
Next, the student combined like terms:
- From \(3x^4\) and \(5x^4\): \(3x^4 + 5x^4 = 8x^4\)
- From \(-8x^2\) and \(2x^2\): \(-8x^2 + 2x^2 = -6x^2\)
- From \(4x\) and \(-9x\): \(4x - 9x = -5x\)

So, the expression becomes:
\[
8x^4 - 6x^2 - 5x
\]
This step is also correct.

### Final Answer:
The final simplified expression given by the student is:
\[
8x^4 - 6x^2 - 5x
\]

### Conclusion:
The student is correct in their work. There were no errors in their steps. The final answer is indeed:
\[
8x^4 - 6x^2 - 5x
\]

Their friend should inform them that they did an excellent job with the polynomial subtraction.