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
![**Title: Polynomial Long Division Example**
**Objective:**
Learn how to divide polynomials using long division.
**Problem:**
Find \(\left(\frac{f}{g}\right)(x)\) using long division for the given functions:
- \(f(x) = x^2 + 8x + 16\)
- \(g(x) = x + 3\)
**Solution Steps:**
1. **Set Up the Division:**
- Write the dividend (\(f(x)\)) and the divisor (\(g(x)\)) in long division format.
2. **Perform the Division:**
- Divide the leading term of the dividend by the leading term of the divisor to get the first term of the quotient.
- Multiply the entire divisor by this term and subtract from the dividend.
- Repeat the process with the new polynomial (remainder) until the degree of the remainder is less than the degree of the divisor.
**Results:**
- The quotient is \([Enter quotient here]\).
- The remainder is \([Enter remainder here]\).
**Conclusion:**
This example demonstrates the process of polynomial long division. The quotient and remainder provide insight into the division of polynomials, essential for understanding algebraic functions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d591113-c73d-4bf8-a1b7-9966513ce440%2F0dd826f1-4f53-4ac2-98a6-d26fd7a0b814%2Fd9ks1x_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Polynomial Long Division Example**
**Objective:**
Learn how to divide polynomials using long division.
**Problem:**
Find \(\left(\frac{f}{g}\right)(x)\) using long division for the given functions:
- \(f(x) = x^2 + 8x + 16\)
- \(g(x) = x + 3\)
**Solution Steps:**
1. **Set Up the Division:**
- Write the dividend (\(f(x)\)) and the divisor (\(g(x)\)) in long division format.
2. **Perform the Division:**
- Divide the leading term of the dividend by the leading term of the divisor to get the first term of the quotient.
- Multiply the entire divisor by this term and subtract from the dividend.
- Repeat the process with the new polynomial (remainder) until the degree of the remainder is less than the degree of the divisor.
**Results:**
- The quotient is \([Enter quotient here]\).
- The remainder is \([Enter remainder here]\).
**Conclusion:**
This example demonstrates the process of polynomial long division. The quotient and remainder provide insight into the division of polynomials, essential for understanding algebraic functions.
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