Question

Question
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.

(2x3−7x2+4x)−(9x−5x3+9x2)

Step 1: 2x3−7x2+4x−9x−5x3+9x2

Step 2: 2x3−5x3−7x2+9x2+4x−9x

Step 3: −3x3+2x2−5x
(2 points)

Answer 1

Let's review each step of Sara's work to check for errors.

### Given Expression:
(2x³ - 7x² + 4x) - (9x - 5x³ + 9x²)

### Step 1:
Sara rewrote the expression as:
2x³ - 7x² + 4x - 9x - 5x³ + 9x²

**Correction:** This step is correct. She has properly distributed the negative sign across the second polynomial.

### Step 2:
Sara then combined like terms:
2x³ - 5x³ - 7x² + 9x² + 4x - 9x

Let's combine the like terms:
- For \(x³\):
\(2x³ - 5x³ = -3x³\)
- For \(x²\):
\(-7x² + 9x² = 2x²\)
- For \(x\):
\(4x - 9x = -5x\)

So the correct combination of like terms should yield:
-3x³ + 2x² - 5x.

**Correction:** This step is also correct.

### Step 3:
Sara concluded with:
−3x³ + 2x² − 5x

**Final Check:** She accurately combined the like terms in the previous step, which means her final answer is indeed correct.

### Conclusion:
Sara's work is correct:
- **Final Answer:** \(−3x³ + 2x² − 5x\)

Her friend should tell her that she made no errors in her work; the solution is correct.