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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![### Synthetic Division of Polynomials
To find the quotient and remainder using synthetic division for the polynomial \(2x^2 - 3x + 2\) divided by \(x - 2\), follow these steps:
1. **Set up the synthetic division:**
- Write down the coefficients of the polynomial \(2x^2 - 3x + 2\): \(2, -3, 2\).
- Write the zero of the divisor \(x - 2\) (solve \(x - 2 = 0\)), which is \(2\).
2. **Perform the synthetic division:**
- Bring down the leading coefficient (\(2\)).
- Multiply this leading coefficient by the zero of the divisor (\(2\)): \(2 \times 2 = 4\).
- Write this product in the next column under the second coefficient (\(-3\)), then add the numbers in this column: \(-3 + 4 = 1\).
- Multiply the resulting number by the zero of the divisor (\(2\)): \(1 \times 2 = 2\).
- Write this product under the next coefficient (\(2\)), then add the numbers in this column: \(2 + 2 = 4\).
3. **Interpret the results:**
- The first row (after bringing down the leading coefficient and performing the multiplications and additions) will yield the coefficients of the quotient.
- The last entry will be the remainder.
Using the synthetic division steps, you will find:
- **Quotient: \(2x + 1\)**
- **Remainder: \(4\)**
**Summary**:
\[ \text{Quotient: } 2x + 1 \]
\[ \text{Remainder: } 4 \]
This synthetic division process helps simplify polynomial divisions efficiently, providing both the quotient and the remainder easily.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04552051-e206-45f1-b504-e01aa8de9423%2F12adf8f0-bef4-4e9d-a021-b2d7d125e3af%2F7pluovf_processed.png&w=3840&q=75)
Transcribed Image Text:### Synthetic Division of Polynomials
To find the quotient and remainder using synthetic division for the polynomial \(2x^2 - 3x + 2\) divided by \(x - 2\), follow these steps:
1. **Set up the synthetic division:**
- Write down the coefficients of the polynomial \(2x^2 - 3x + 2\): \(2, -3, 2\).
- Write the zero of the divisor \(x - 2\) (solve \(x - 2 = 0\)), which is \(2\).
2. **Perform the synthetic division:**
- Bring down the leading coefficient (\(2\)).
- Multiply this leading coefficient by the zero of the divisor (\(2\)): \(2 \times 2 = 4\).
- Write this product in the next column under the second coefficient (\(-3\)), then add the numbers in this column: \(-3 + 4 = 1\).
- Multiply the resulting number by the zero of the divisor (\(2\)): \(1 \times 2 = 2\).
- Write this product under the next coefficient (\(2\)), then add the numbers in this column: \(2 + 2 = 4\).
3. **Interpret the results:**
- The first row (after bringing down the leading coefficient and performing the multiplications and additions) will yield the coefficients of the quotient.
- The last entry will be the remainder.
Using the synthetic division steps, you will find:
- **Quotient: \(2x + 1\)**
- **Remainder: \(4\)**
**Summary**:
\[ \text{Quotient: } 2x + 1 \]
\[ \text{Remainder: } 4 \]
This synthetic division process helps simplify polynomial divisions efficiently, providing both the quotient and the remainder easily.
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