- Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) and express P(x) in the form d(x) • Q(x) + R(x). P(x)= x³ +5x² - 2x +176 d(x)=x+8 P(X) = (x+8) +
- Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x) and express P(x) in the form d(x) • Q(x) + R(x). P(x)= x³ +5x² - 2x +176 d(x)=x+8 P(X) = (x+8) +
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
![**Long Division of Polynomials**
Use long division to find the quotient \( Q(x) \) and the remainder \( R(x) \) when \( P(x) \) is divided by \( d(x) \). Express \( P(x) \) in the form \( d(x) \cdot Q(x) + R(x) \).
Given:
\[ P(x) = x^3 + 5x^2 - 2x + 176 \]
\[ d(x) = x + 8 \]
To perform the division, set up the expression:
\[ P(x) = (x + 8) \left(\text{Quotient}\right) + \text{Remainder} \]
Follow these steps to solve:
1. **Divide the leading term of \( P(x) \) by the leading term of \( d(x) \)**.
2. **Multiply the entire divisor \( d(x) \) by this result** and subtract from \( P(x) \).
3. **Repeat the process** with the new polynomial formed after subtraction until the degree of the remaining polynomial is less than the degree of \( d(x) \).
This helps in finding the complete polynomial division where \( P(x) = d(x) \cdot Q(x) + R(x) \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f78fe67-9f65-4591-abf6-cb97fc8e35e5%2F100ffb77-33fe-48c0-8246-2eaf78b29c2c%2Fg47qrua_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Long Division of Polynomials**
Use long division to find the quotient \( Q(x) \) and the remainder \( R(x) \) when \( P(x) \) is divided by \( d(x) \). Express \( P(x) \) in the form \( d(x) \cdot Q(x) + R(x) \).
Given:
\[ P(x) = x^3 + 5x^2 - 2x + 176 \]
\[ d(x) = x + 8 \]
To perform the division, set up the expression:
\[ P(x) = (x + 8) \left(\text{Quotient}\right) + \text{Remainder} \]
Follow these steps to solve:
1. **Divide the leading term of \( P(x) \) by the leading term of \( d(x) \)**.
2. **Multiply the entire divisor \( d(x) \) by this result** and subtract from \( P(x) \).
3. **Repeat the process** with the new polynomial formed after subtraction until the degree of the remaining polynomial is less than the degree of \( d(x) \).
This helps in finding the complete polynomial division where \( P(x) = d(x) \cdot Q(x) + R(x) \).
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