Question

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?(2x3−7x2+4x)−(9x−5x3+9x2)(2𝑥3−7𝑥2+4𝑥)−(9𝑥−5𝑥3+9𝑥2)Step 1: 2x3−7x2+4x−9x−5x3+9x22𝑥3−7𝑥2+4𝑥−9𝑥−5𝑥3+9𝑥2Step 2: 2x3−5x3−7x2+9x2+4x−9x2𝑥3−5𝑥3−7𝑥2+9𝑥2+4𝑥−9𝑥Step 3: −3x3+2x2−5x−3𝑥3+2𝑥2−5𝑥Final Answer: −3x3+2x2−5x−3𝑥3+2𝑥2−5𝑥(1 point)ResponsesThe student is correctThe student is correctThe student is incorrect

Answer 1

To determine whether the student is correct, let's look at their work step by step.

1. **Original expression**:
\((2x^3 - 7x^2 + 4x) - (9x - 5x^3 + 9x^2)\)

2. **Step 1**:
Distribute the negative sign correctly:

\[
2x^3 - 7x^2 + 4x - 9x + 5x^3 - 9x^2
\]

This is the correct rearrangement.

3. **Step 2**:
Combine like terms:
- For \(x^3\): \(2x^3 + 5x^3 = 7x^3\)
- For \(x^2\): \(-7x^2 - 9x^2 = -16x^2\)
- For \(x\): \(4x - 9x = -5x\)

Correctly combining them, we should have:

\[
(2x^3 + 5x^3) + (-7x^2 - 9x^2) + (4x - 9x) = 7x^3 - 16x^2 - 5x
\]

4. **Step 3**:
The final answer should be:

\[
7x^3 - 16x^2 - 5x
\]

The student's final answer was \(-3x^3 + 2x^2 - 5x\). Clearly, there is a discrepancy.

**Conclusion**:
The student is **incorrect**. They made the error in **Step 2** when combining like terms. The correct coefficients, after correctly arranging the terms, should yield \(7x^3 - 16x^2 - 5x\) instead of \(-3x^3 + 2x^2 - 5x\).