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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![**Problem:**
Solve the polynomial division:
\[ \frac{(4x^3 + 5x - 3)}{(x + 1)} \]
**Instructions:**
The problem requires you to perform a division of the cubic polynomial \(4x^3 + 5x - 3\) by the linear polynomial \(x + 1\). Use polynomial long division or synthetic division to find the quotient and remainder.
**Guidance:**
1. **Identify the divisor and dividend**:
- Dividend: \(4x^3 + 5x - 3\)
- Divisor: \(x + 1\)
2. **Perform Polynomial Long Division**:
- Divide the first term of the dividend by the first term of the divisor.
- Multiply the entire divisor by this result and subtract from the dividend.
- Repeat the process with the new polynomial formed after subtraction.
3. **Verify your result**:
- Multiply the quotient by the divisor and add the remainder to ensure it matches the original dividend.
This solution approach will give insight into polynomial division, a key concept in algebra.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fe4e0d9-a441-4076-9243-8e98c4a90bfe%2F7f82e23b-79c1-45a6-a076-ade86523f835%2F9i063zq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem:**
Solve the polynomial division:
\[ \frac{(4x^3 + 5x - 3)}{(x + 1)} \]
**Instructions:**
The problem requires you to perform a division of the cubic polynomial \(4x^3 + 5x - 3\) by the linear polynomial \(x + 1\). Use polynomial long division or synthetic division to find the quotient and remainder.
**Guidance:**
1. **Identify the divisor and dividend**:
- Dividend: \(4x^3 + 5x - 3\)
- Divisor: \(x + 1\)
2. **Perform Polynomial Long Division**:
- Divide the first term of the dividend by the first term of the divisor.
- Multiply the entire divisor by this result and subtract from the dividend.
- Repeat the process with the new polynomial formed after subtraction.
3. **Verify your result**:
- Multiply the quotient by the divisor and add the remainder to ensure it matches the original dividend.
This solution approach will give insight into polynomial division, a key concept in algebra.
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