Possible Reatlional zerros = Ys, b. Below is a graph of P(x). Based on the graph, determine which of the possible rational zeros actually turn out to be zeros. y 4
Possible Reatlional zerros = Ys, b. Below is a graph of P(x). Based on the graph, determine which of the possible rational zeros actually turn out to be zeros. y 4
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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![**Transcription for Educational Website**
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**Title: Analyzing Possible Rational Zeros from Polynomial Graphs**
In this exercise, we will identify the possible rational zeros of the polynomial \( P(x) \) by analyzing its graph.
**Instructions:**
1. **Identifying Fraction of Constant Term:**
The possible rational zeros can be found using the fraction of the constant term, indicated by the expression:
\[
\text{Fraction of constant form} = \pm \frac{1}{\text{leading coefficient}}
\]
This leads to the possible rational zeros:
\[
\pm 1, \pm \frac{1}{1}, \pm \frac{1}{5}
\]
2. **Graph Interpretation:**
Below is a graph of \( P(x) \). Using the graph, we will determine which of these possible rational zeros actually correspond to the zeros of the polynomial.
The graph shows a red polynomial curve on an \( xy \)-plane:
- The curve crosses the \( x \)-axis at approximately \( x = -1 \), \( x = 0 \), and \( x = 1 \).
- This indicates the actual rational zeros are likely among the listed possibilities.
**Conclusion:**
By observing the points where the graph intersects the \( x \)-axis, we can confirm the actual rational zeros. This is an essential technique in polynomial analysis, aiding in solving and simplifying equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b1f3c36-1e14-44e7-87e6-2541b6740659%2F4b335034-6c8e-4bd5-9c39-b0581f386a7e%2Fbmztyw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website**
---
**Title: Analyzing Possible Rational Zeros from Polynomial Graphs**
In this exercise, we will identify the possible rational zeros of the polynomial \( P(x) \) by analyzing its graph.
**Instructions:**
1. **Identifying Fraction of Constant Term:**
The possible rational zeros can be found using the fraction of the constant term, indicated by the expression:
\[
\text{Fraction of constant form} = \pm \frac{1}{\text{leading coefficient}}
\]
This leads to the possible rational zeros:
\[
\pm 1, \pm \frac{1}{1}, \pm \frac{1}{5}
\]
2. **Graph Interpretation:**
Below is a graph of \( P(x) \). Using the graph, we will determine which of these possible rational zeros actually correspond to the zeros of the polynomial.
The graph shows a red polynomial curve on an \( xy \)-plane:
- The curve crosses the \( x \)-axis at approximately \( x = -1 \), \( x = 0 \), and \( x = 1 \).
- This indicates the actual rational zeros are likely among the listed possibilities.
**Conclusion:**
By observing the points where the graph intersects the \( x \)-axis, we can confirm the actual rational zeros. This is an essential technique in polynomial analysis, aiding in solving and simplifying equations.
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