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.
Topic Video
Question
7
![### Polynomial Division Problem
#### Question 7:
**Find the quotient:**
\[ (6x^3 + 3x + 70) \div (x + 4) \]
**Your answer:**
*________________*
---
#### Explanation
This question involves polynomial long division. You are asked to divide the polynomial \( 6x^3 + 3x + 70 \) by the binomial \( x + 4 \).
To solve this:
1. **Setup the Division:**
- Write \( 6x^3 + 3x + 70 \) under the division symbol.
- Write \( x + 4 \) outside the division symbol.
2. **Divide the Leading Terms:**
- Divide the leading term of the numerator \( 6x^3 \) by the leading term of the denominator \( x \) to get \( 6x^2 \).
3. **Multiply and Subtract:**
- Multiply \( 6x^2 \) by \( x + 4 \) and subtract the result from the original polynomial.
- Repeat the process with the new polynomial obtained after subtraction.
4. **Continue Until No Further Division is Possible.**
This method will eventually yield the quotient and potentially a remainder if \( x + 4 \) does not divide the original polynomial evenly.
Understanding polynomial long division is crucial for simplifying polynomials in algebra. It is similar to the long division method used in arithmetic but involves variables.
---
#### Question 8:
**Given the following set of data:**
15, 13, 9, 9, 9, 7, 1, 1, ...
(*Note:* The remaining part of Question 8 is cut off in the image, hence not fully transcribed.)
---
#### Graphs and Diagrams:
There are no graphs or diagrams provided in the image.
---
This transcription is designed to help students understand and solve polynomial division problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4ebf58c8-d1d0-4c50-9c0f-0d63550ccd98%2F057c9b40-d8b7-40a3-9d7e-973affbd5727%2Fyiauj59_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Polynomial Division Problem
#### Question 7:
**Find the quotient:**
\[ (6x^3 + 3x + 70) \div (x + 4) \]
**Your answer:**
*________________*
---
#### Explanation
This question involves polynomial long division. You are asked to divide the polynomial \( 6x^3 + 3x + 70 \) by the binomial \( x + 4 \).
To solve this:
1. **Setup the Division:**
- Write \( 6x^3 + 3x + 70 \) under the division symbol.
- Write \( x + 4 \) outside the division symbol.
2. **Divide the Leading Terms:**
- Divide the leading term of the numerator \( 6x^3 \) by the leading term of the denominator \( x \) to get \( 6x^2 \).
3. **Multiply and Subtract:**
- Multiply \( 6x^2 \) by \( x + 4 \) and subtract the result from the original polynomial.
- Repeat the process with the new polynomial obtained after subtraction.
4. **Continue Until No Further Division is Possible.**
This method will eventually yield the quotient and potentially a remainder if \( x + 4 \) does not divide the original polynomial evenly.
Understanding polynomial long division is crucial for simplifying polynomials in algebra. It is similar to the long division method used in arithmetic but involves variables.
---
#### Question 8:
**Given the following set of data:**
15, 13, 9, 9, 9, 7, 1, 1, ...
(*Note:* The remaining part of Question 8 is cut off in the image, hence not fully transcribed.)
---
#### Graphs and Diagrams:
There are no graphs or diagrams provided in the image.
---
This transcription is designed to help students understand and solve polynomial division problems.
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