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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Question
Algebra Question 10.10
![**Transcription for Educational Website:**
**Title:** Polynomial Factoring Exercise
**Instruction:**
Write an expression in factored form for the polynomial of least possible degree graphed below.
**Graph Description:**
The graph shows a polynomial curve intersecting the x-axis at three points: approximately \(x = -3\), \(x = 0\), and \(x = 2\). The polynomial appears to be a cubic function as it changes direction twice. The behavior of the polynomial suggests that it has at least one repeated root or a combination of single roots based on its points of tangency.
The curve descends from the left, crosses the x-axis at \(x \approx -3\), descends again to a minimum below the x-axis, and rises to intersect the x-axis at \(x = 0\). It then rises to a local maximum and descends once more before crossing the x-axis at \(x \approx 2\) and then increasing as it moves to the right.
**y(x) =** [Input box for student to provide the polynomial expression]
**Graph Features:**
- X-axis range: -5 to 5
- Y-axis range: -6 to 6
- Key features to consider: x-intercepts indicating factors, points of tangency indicating repeated roots, and changes in direction highlighting the degree of the polynomial.
**Purpose:**
The exercise aims to reinforce understanding of polynomial characteristics, particularly factoring into roots, by interpreting graphical data.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff76447b6-9a79-40f3-b9ba-1d0612675f50%2F918a875f-c9d9-4def-96d8-8ceb1ed0842d%2Fmn4s3thw_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
**Title:** Polynomial Factoring Exercise
**Instruction:**
Write an expression in factored form for the polynomial of least possible degree graphed below.
**Graph Description:**
The graph shows a polynomial curve intersecting the x-axis at three points: approximately \(x = -3\), \(x = 0\), and \(x = 2\). The polynomial appears to be a cubic function as it changes direction twice. The behavior of the polynomial suggests that it has at least one repeated root or a combination of single roots based on its points of tangency.
The curve descends from the left, crosses the x-axis at \(x \approx -3\), descends again to a minimum below the x-axis, and rises to intersect the x-axis at \(x = 0\). It then rises to a local maximum and descends once more before crossing the x-axis at \(x \approx 2\) and then increasing as it moves to the right.
**y(x) =** [Input box for student to provide the polynomial expression]
**Graph Features:**
- X-axis range: -5 to 5
- Y-axis range: -6 to 6
- Key features to consider: x-intercepts indicating factors, points of tangency indicating repeated roots, and changes in direction highlighting the degree of the polynomial.
**Purpose:**
The exercise aims to reinforce understanding of polynomial characteristics, particularly factoring into roots, by interpreting graphical data.
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