Sara subtracted two polynomials. She asked a friend to check her solution and work. What should her friend tell her? Is Sara correct? If she is not correct, explain which step the error was made AND what the error was.

Let's check Sara's work step by step to see if there are any errors:

**Step 1: Write the expression correctly.**
Sara wrote:
\[
(2x^3−7x^2+4x)−(9x−5x^3+9x^2)
\]
This step is correct as it properly combines the polynomials by rewriting it as:
\[
2x^3−7x^2+4x−9x−5x^3+9x^2
\]

**Step 2: Combine like terms.**
In this step, she rearranged the terms:
\[
2x^3−5x^3−7x^2+9x^2+4x−9x
\]
This step is also correct in terms of grouping the terms.

**Step 3: Perform the actual arithmetic for combining like terms.**
Now, let's perform the arithmetic on the grouped terms:

1. For the \(x^3\) terms:
\[
2x^3 - 5x^3 = -3x^3
\]

2. For the \(x^2\) terms:
\[
-7x^2 + 9x^2 = 2x^2
\]

3. For the \(x\) terms:
\[
4x - 9x = -5x
\]

So, combining all these gives us:
\[
-3x^3 + 2x^2 - 5x
\]

**Conclusion:**
Sara's final result in Step 3 is correct. Her calculations show that she combined the terms properly and arrived at the correct final polynomial.

Her friend should tell her that she is correct, and there were no errors in her work.