**Problem Statement:**Subtract the polynomials and simplify the result completely:\[(-3x^5 + 7x^4 - 4x - 6) - (-12x^5 - 8x^4 - x^3 + x)\]**Solution:**1. **Distribute the Negative Sign:** \[ (-3x^5 + 7x^4 - 4x - 6) + (12x^5 + 8x^4 + x^3 - x) \]2. **Combine Like Terms:** - **For \(x^5\):** \(-3x^5 + 12x^5 = 9x^5\) - **For \(x^4\):** \(7x^4 + 8x^4 = 15x^4\) - **For \(x^3\):** \(x^3\) - **For \(x\):** \(-4x - x = -5x\) - **Constant Terms:** \(-6\)3. **Final Simplified Polynomial:** \[ 9x^5 + 15x^4 + x^3 - 5x - 6 \]This is the complete simplified result of subtracting the given polynomials.

Answered: Subtract the polynomials and simplify…

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Subtract the polynomials and simplify the result completely: (- 3x° + 7xª – 4x – 6) – (– 12z" – 8a* – 2° + x)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

**Problem Statement:**

Subtract the polynomials and simplify the result completely:

\[
(-3x^5 + 7x^4 - 4x - 6) - (-12x^5 - 8x^4 - x^3 + x)
\]

**Solution:**

1. **Distribute the Negative Sign:**
\[
(-3x^5 + 7x^4 - 4x - 6) + (12x^5 + 8x^4 + x^3 - x)
\]

2. **Combine Like Terms:**
- **For \(x^5\):** \(-3x^5 + 12x^5 = 9x^5\)
- **For \(x^4\):** \(7x^4 + 8x^4 = 15x^4\)
- **For \(x^3\):** \(x^3\)
- **For \(x\):** \(-4x - x = -5x\)
- **Constant Terms:** \(-6\)

3. **Final Simplified Polynomial:**
\[
9x^5 + 15x^4 + x^3 - 5x - 6
\]

This is the complete simplified result of subtracting the given polynomials.

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