Let's go through Sara's steps and verify her work on the subtraction of the polynomials.
We start with the expression:
\[
(2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2)
\]
### Step 1:
Sara rewrites the expression:
\[
2x^3 - 7x^2 + 4x - 9x + 5x^3 - 9x^2
\]
The second polynomial is distributed correctly (the negative sign is applied), so this step is correct.
### Step 2:
In this step, she combines like terms:
\[
2x^3 - 5x^3 - 7x^2 + 9x^2 + 4x - 9x
\]
This notation is also correct; she is gathering the terms correctly according to their degrees.
### Step 3:
Now, she combines the coefficients:
1. Combine \(2x^3\) and \(-5x^3\):
\[
2x^3 - 5x^3 = -3x^3
\]
2. Combine \(-7x^2\) and \(9x^2\):
\[
-7x^2 + 9x^2 = 2x^2
\]
3. Combine \(4x\) and \(-9x\):
\[
4x - 9x = -5x
\]
Thus, the final combined polynomial is:
\[
-3x^3 + 2x^2 - 5x
\]
### Conclusion:
Sara's final result in Step 3:
\[
-3x^3 + 2x^2 - 5x
\]
is indeed correct based on her work in the previous steps.
**Her friend should tell her she is correct with her results, as there are no mistakes in the steps shown.**