Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
![### Polynomial Division Example
**Problem:**
Divide using the long division process:
\[
(x^3 - 7x^2 + 2x + 17) \div (x + 3)
\]
**Solution:**
The image shows the work involved in using polynomial long division. Here’s an explanation of how to perform the division:
1. **Setup the Division:**
- The divisor is \(x + 3\).
- The dividend is \(x^3 - 7x^2 + 2x + 17\).
2. **First Division:**
- Divide the leading term of the dividend \(x^3\) by the leading term of the divisor \(x\), which gives \(x^2\).
- Multiply the entire divisor \(x + 3\) by \(x^2\) and write the result \((x^3 + 3x^2)\) under the dividend.
- Subtract to find the new dividend, which will be \((-10x^2 + 2x + 17)\).
3. **Second Division:**
- Divide the new leading term \(-10x^2\) by \(x\), which gives \(-10x\).
- Multiply the entire divisor by \(-10x\) and write the result under the new dividend.
- Subtract to find the next dividend, which will be \((32x + 17)\).
4. **Third Division:**
- Divide the new leading term \(32x\) by \(x\), which gives \(32\).
- Multiply the entire divisor \(x + 3\) by \(32\) and write the result under the new dividend.
- Subtract to find the final remainder, which will be \( -79 \).
**Final Result:**
The quotient is \(x^2 - 10x + 32\) with a remainder of \(-79\).
This step-by-step process illustrates how polynomial long division is performed. It mirrors the long division process used with numbers but with polynomial terms instead.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb54d9a9-2037-418c-ad8a-976bf23f5d59%2Fa1f75e91-4c8e-460b-879f-a3f32ed68b5c%2Fcoq8skt.jpeg&w=3840&q=75)
Transcribed Image Text:### Polynomial Division Example
**Problem:**
Divide using the long division process:
\[
(x^3 - 7x^2 + 2x + 17) \div (x + 3)
\]
**Solution:**
The image shows the work involved in using polynomial long division. Here’s an explanation of how to perform the division:
1. **Setup the Division:**
- The divisor is \(x + 3\).
- The dividend is \(x^3 - 7x^2 + 2x + 17\).
2. **First Division:**
- Divide the leading term of the dividend \(x^3\) by the leading term of the divisor \(x\), which gives \(x^2\).
- Multiply the entire divisor \(x + 3\) by \(x^2\) and write the result \((x^3 + 3x^2)\) under the dividend.
- Subtract to find the new dividend, which will be \((-10x^2 + 2x + 17)\).
3. **Second Division:**
- Divide the new leading term \(-10x^2\) by \(x\), which gives \(-10x\).
- Multiply the entire divisor by \(-10x\) and write the result under the new dividend.
- Subtract to find the next dividend, which will be \((32x + 17)\).
4. **Third Division:**
- Divide the new leading term \(32x\) by \(x\), which gives \(32\).
- Multiply the entire divisor \(x + 3\) by \(32\) and write the result under the new dividend.
- Subtract to find the final remainder, which will be \( -79 \).
**Final Result:**
The quotient is \(x^2 - 10x + 32\) with a remainder of \(-79\).
This step-by-step process illustrates how polynomial long division is performed. It mirrors the long division process used with numbers but with polynomial terms instead.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning