List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). (Enter your answers as a comma-separated li P(x) = x - 8x2 + 7
List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). (Enter your answers as a comma-separated li P(x) = x - 8x2 + 7
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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![**Title: Finding Possible Rational Zeros using the Rational Zeros Theorem**
**Instructions:**
List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). Enter your answers as a comma-separated list.
**Problem Statement:**
Given the polynomial function:
\[ P(x) = x^3 - 8x^2 + 7 \]
**Input Field:**
\[ x = \text{[ ]}\]
**Explanation:**
The Rational Zeros Theorem states that any possible rational zero of the polynomial \(P(x)\) is a ratio of the factors of the constant term to the factors of the leading coefficient. In this case, the constant term is \(7\) and the leading coefficient is \(1\).
**Steps to Solve:**
1. Identify the constant term (c) and the leading coefficient (a) from the polynomial \(P(x)\).
- For \(P(x) = x^3 - 8x^2 + 7\), the constant term \(c = 7\) and the leading coefficient \(a = 1\).
2. List all factors of the constant term \(c\) and the leading coefficient \(a\):
- Factors of 7: \( \pm 1, \pm 7\)
- Factors of 1: \( \pm 1\)
3. Form all possible rational zeros by taking ratios of the factors of the constant term to the factors of the leading coefficient:
- Possible rational zeros: \( \pm \frac{1}{1}, \pm \frac{7}{1}\)
4. Simplify the ratios to get the list of potential rational zeros:
- Possible rational zeros: \(\pm 1, \pm 7\)
**Your Task:**
Enter the possible rational zeros as a comma-separated list in the input field provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f4719ec-89c6-49f2-a8fd-c905fe776b01%2F88997c96-da7b-4935-89fd-686f9fd24c76%2Fsuqlna_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Finding Possible Rational Zeros using the Rational Zeros Theorem**
**Instructions:**
List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros). Enter your answers as a comma-separated list.
**Problem Statement:**
Given the polynomial function:
\[ P(x) = x^3 - 8x^2 + 7 \]
**Input Field:**
\[ x = \text{[ ]}\]
**Explanation:**
The Rational Zeros Theorem states that any possible rational zero of the polynomial \(P(x)\) is a ratio of the factors of the constant term to the factors of the leading coefficient. In this case, the constant term is \(7\) and the leading coefficient is \(1\).
**Steps to Solve:**
1. Identify the constant term (c) and the leading coefficient (a) from the polynomial \(P(x)\).
- For \(P(x) = x^3 - 8x^2 + 7\), the constant term \(c = 7\) and the leading coefficient \(a = 1\).
2. List all factors of the constant term \(c\) and the leading coefficient \(a\):
- Factors of 7: \( \pm 1, \pm 7\)
- Factors of 1: \( \pm 1\)
3. Form all possible rational zeros by taking ratios of the factors of the constant term to the factors of the leading coefficient:
- Possible rational zeros: \( \pm \frac{1}{1}, \pm \frac{7}{1}\)
4. Simplify the ratios to get the list of potential rational zeros:
- Possible rational zeros: \(\pm 1, \pm 7\)
**Your Task:**
Enter the possible rational zeros as a comma-separated list in the input field provided.
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