Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
find the rational zeros of the function (use rational zero tests with steps)
![## Polynomial Equations: Finding Rational Zeros
Listed below are polynomial functions for which you need to find the rational zeros. Each function is a cubic polynomial, which means it includes terms up to \( x^3 \).
1. **Function 1:**
\[
f(x) = x^3 - 7x - 6
\]
2. **Function 2:**
\[
f(x) = x^3 - 13x + 12
\]
3. **Function 3:**
\[
f(x) = x^3 - 4x^2 - x + 4
\]
4. **Function 4:**
\[
f(x) = x^3 - 9x^2 + 20x - 12
\]
5. **Function 5:**
\[
f(x) = x^3 + 8x^2 + 13x + 6
\]
6. **Function 6:**
\[
f(x) = x^3 - 9x^2 + 27x - 27
\]
7. **Function 7:**
\[
f(x) = 2x^3 + 3x^2 - 1
\]
These problems focus on identifying the rational zeros of each cubic equation. Use techniques such as the Rational Root Theorem, synthetic division, or graphing to find the rational solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90b2ad7e-71be-4993-92e0-fe2030354ee3%2Fa6a85a70-b51b-49f6-b1d0-cd869e913eb8%2Fv08kc4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Polynomial Equations: Finding Rational Zeros
Listed below are polynomial functions for which you need to find the rational zeros. Each function is a cubic polynomial, which means it includes terms up to \( x^3 \).
1. **Function 1:**
\[
f(x) = x^3 - 7x - 6
\]
2. **Function 2:**
\[
f(x) = x^3 - 13x + 12
\]
3. **Function 3:**
\[
f(x) = x^3 - 4x^2 - x + 4
\]
4. **Function 4:**
\[
f(x) = x^3 - 9x^2 + 20x - 12
\]
5. **Function 5:**
\[
f(x) = x^3 + 8x^2 + 13x + 6
\]
6. **Function 6:**
\[
f(x) = x^3 - 9x^2 + 27x - 27
\]
7. **Function 7:**
\[
f(x) = 2x^3 + 3x^2 - 1
\]
These problems focus on identifying the rational zeros of each cubic equation. Use techniques such as the Rational Root Theorem, synthetic division, or graphing to find the rational solutions.
![## Polynomial Functions
### Problem 8
\[ f(x) = 3x^3 - 19x^2 + 33x - 9 \]
This function is a cubic polynomial, which is of degree three. It includes three terms with varying powers of \(x\) and a constant term.
### Problem 9
\[ f(x) = 9x^4 - 9x^3 - 58x^2 + 4x + 24 \]
This function is a quartic polynomial, which is of degree four. It includes four terms with varying powers of \(x\) and a constant term.
### Problem 10
\[ f(x) = 2x^4 - 15x^3 + 23x^2 + 15x - 25 \]
This function is also a quartic polynomial, similar to Problem 9. It contains four terms with varying powers of \(x\) and a constant term.
These polynomials can be used to model various real-world scenarios, allowing for the analysis of complex relationships between variables.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90b2ad7e-71be-4993-92e0-fe2030354ee3%2Fa6a85a70-b51b-49f6-b1d0-cd869e913eb8%2Fpdpmxyh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Polynomial Functions
### Problem 8
\[ f(x) = 3x^3 - 19x^2 + 33x - 9 \]
This function is a cubic polynomial, which is of degree three. It includes three terms with varying powers of \(x\) and a constant term.
### Problem 9
\[ f(x) = 9x^4 - 9x^3 - 58x^2 + 4x + 24 \]
This function is a quartic polynomial, which is of degree four. It includes four terms with varying powers of \(x\) and a constant term.
### Problem 10
\[ f(x) = 2x^4 - 15x^3 + 23x^2 + 15x - 25 \]
This function is also a quartic polynomial, similar to Problem 9. It contains four terms with varying powers of \(x\) and a constant term.
These polynomials can be used to model various real-world scenarios, allowing for the analysis of complex relationships between variables.
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