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
100%
![### Example Problem: Finding the Sum of Polynomials
To find the sum of two polynomials, you add the corresponding coefficients of each term. Let's use the following polynomials as an example:
**Given Polynomials:**
\[8x^3 - 3x^2 + 4x - 8\]
\[+ (-9x^3 - 2x^2 - 5x + 5)\]
Follow these steps to find their sum:
1. **Align Coefficients:**
Place the polynomials so that like terms (terms with the same exponent) are aligned:
\[
\begin{array}{r}
8x^3 - 3x^2 + 4x - 8 \\
+ (-9x^3 - 2x^2 - 5x + 5) \\
\end{array}
\]
2. **Add Like Terms:**
Add the coefficients of the like terms.
- For \(x^3\) terms: \(8x^3 + (-9x^3) = -1x^3\)
- For \(x^2\) terms: \(-3x^2 + (-2x^2) = -5x^2\)
- For \(x\) terms: \(4x + (-5x) = -1x\)
- Constant terms: \(-8 + 5 = -3\)
Now, combine the results:
\[
-1x^3 - 5x^2 - 1x - 3
\]
3. **Write the Final Sum:**
The sum of the polynomials is:
\[
-x^3 - 5x^2 - x - 3
\]
Using these steps, you can find the sum of any two polynomials by aligning like terms and then adding their coefficients.
Approach problems like these systematically, and you'll find the addition of polynomials to be straightforward!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c02ecae-9f3c-4011-90ce-878cb1c02c8e%2F33a668f1-cbf6-4a01-a7ef-1070cfac3d32%2Fbivzi8b_processed.png&w=3840&q=75)
Transcribed Image Text:### Example Problem: Finding the Sum of Polynomials
To find the sum of two polynomials, you add the corresponding coefficients of each term. Let's use the following polynomials as an example:
**Given Polynomials:**
\[8x^3 - 3x^2 + 4x - 8\]
\[+ (-9x^3 - 2x^2 - 5x + 5)\]
Follow these steps to find their sum:
1. **Align Coefficients:**
Place the polynomials so that like terms (terms with the same exponent) are aligned:
\[
\begin{array}{r}
8x^3 - 3x^2 + 4x - 8 \\
+ (-9x^3 - 2x^2 - 5x + 5) \\
\end{array}
\]
2. **Add Like Terms:**
Add the coefficients of the like terms.
- For \(x^3\) terms: \(8x^3 + (-9x^3) = -1x^3\)
- For \(x^2\) terms: \(-3x^2 + (-2x^2) = -5x^2\)
- For \(x\) terms: \(4x + (-5x) = -1x\)
- Constant terms: \(-8 + 5 = -3\)
Now, combine the results:
\[
-1x^3 - 5x^2 - 1x - 3
\]
3. **Write the Final Sum:**
The sum of the polynomials is:
\[
-x^3 - 5x^2 - x - 3
\]
Using these steps, you can find the sum of any two polynomials by aligning like terms and then adding their coefficients.
Approach problems like these systematically, and you'll find the addition of polynomials to be straightforward!
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education