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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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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![### Synthetic Division Example
#### Problem:
Divide using synthetic division.
\[ \frac{2x^5 - 4x^4 + 3x^3 + 4x^2 - 3x + 4}{x + 2} \]
---
To solve this polynomial division problem using synthetic division, follow these steps:
1. **Write down the coefficients of the dividend polynomial**: \( 2, -4, 3, 4, -3, 4 \).
2. **Identify the zero of the divisor** \( x + 2 \): The zero is \(-2\).
3. **Set up the synthetic division table**: Place \(-2\) on the left, and all coefficients of the dividend in a row.
Here’s a detailed step-by-step process to perform synthetic division with this setup:
\[
\begin{array}{r|rrrrrr}
-2 & 2 & -4 & 3 & 4 & -3 & 4 \\
\hline
& & -4 & 12 & -30 & 68 & -142 \\
\hline
& 2 & -8 & 11 & -22 & 44 & -138 \\
\end{array}
\]
- **Step 1**: Bring down the first coefficient \(2\) directly under the line.
- **Step 2**: Multiply \(2\) by \(-2\) (the zero of the divisor) to get \(-4\), then write it under the next coefficient \(-4\).
- **Step 3**: Add \(-4\) and \(-4\) to get \(-8\).
- **Step 4**: Multiply \(-8\) by \(-2\) to get \(16\), then place it under the next coefficient \(3\).
- **Step 5**: Add \(3\) and \(16\) to get \(11\).
- **Step 6**: Continue this process until the last coefficient is processed.
The final row \(2, -8, 11, -22, 44, -138\) represents the coefficients of the quotient polynomial and the remainder.
Hence, the quotient from synthetic division is:
\[ 2x^4 - 8x^3 + 11x^2 - 22x +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd24806a3-11d6-4411-a674-dfa92f3b229c%2F8f8a754a-1b88-49c9-b86f-f5cad0d1f997%2Fhqmu459.jpeg&w=3840&q=75)
Transcribed Image Text:### Synthetic Division Example
#### Problem:
Divide using synthetic division.
\[ \frac{2x^5 - 4x^4 + 3x^3 + 4x^2 - 3x + 4}{x + 2} \]
---
To solve this polynomial division problem using synthetic division, follow these steps:
1. **Write down the coefficients of the dividend polynomial**: \( 2, -4, 3, 4, -3, 4 \).
2. **Identify the zero of the divisor** \( x + 2 \): The zero is \(-2\).
3. **Set up the synthetic division table**: Place \(-2\) on the left, and all coefficients of the dividend in a row.
Here’s a detailed step-by-step process to perform synthetic division with this setup:
\[
\begin{array}{r|rrrrrr}
-2 & 2 & -4 & 3 & 4 & -3 & 4 \\
\hline
& & -4 & 12 & -30 & 68 & -142 \\
\hline
& 2 & -8 & 11 & -22 & 44 & -138 \\
\end{array}
\]
- **Step 1**: Bring down the first coefficient \(2\) directly under the line.
- **Step 2**: Multiply \(2\) by \(-2\) (the zero of the divisor) to get \(-4\), then write it under the next coefficient \(-4\).
- **Step 3**: Add \(-4\) and \(-4\) to get \(-8\).
- **Step 4**: Multiply \(-8\) by \(-2\) to get \(16\), then place it under the next coefficient \(3\).
- **Step 5**: Add \(3\) and \(16\) to get \(11\).
- **Step 6**: Continue this process until the last coefficient is processed.
The final row \(2, -8, 11, -22, 44, -138\) represents the coefficients of the quotient polynomial and the remainder.
Hence, the quotient from synthetic division is:
\[ 2x^4 - 8x^3 + 11x^2 - 22x +
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