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,...
Related questions
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d591113-c73d-4bf8-a1b7-9966513ce440%2F6b54df9c-611a-4a98-a76a-de07377ae0e0%2Fc8e32u9_processed.png&w=3840&q=75)
Transcribed Image Text:**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.
Expert Solution
Step 1
To find the answer open the bracket and subtract the coefficients of the same degree then simplify.
Step by step
Solved in 2 steps with 1 images
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