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16. Find the "complete" factored form, including the leading coeffi polynomial, g(x), shown in the graph below. -8 9 L 10 8 6 2 2 -8 2

16. Find the "complete" factored form, including the leading coeffi polynomial, g(x), shown in the graph below. -8 9 L 10 8 6 2 2 -8 2

Calculus: Early Transcendentals
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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## Problem Statement 16. Find the "complete" factored form, including the leading coefficient, of the 6th-degree polynomial, \( g(x) \), shown in the graph below. ## Graph Analysis The graph depicts a polynomial function with the following characteristics: - **Degree**: 6th degree, as indicated in the problem statement. - **Behavior at Infinity**: The graph rises to positive infinity on both the left and right extremes, indicating a positive leading coefficient. ### Key Features: - **Intercepts**: The graph intersects the x-axis at \( x \approx -6, -3, \) and \( 1 \). - **Turning Points**: The polynomial has several turning points, consistent with it being a 6th-degree polynomial. ### End Behavior: - As \( x \to -\infty \), \( g(x) \to \infty \) - As \( x \to \infty \), \( g(x) \to \infty \) ## Conclusion To find the complete factored form of the polynomial, consider the x-intercepts and the behavior of the graph. Note that further analysis, such as determining multiplicities and verifying with algebraic methods or technology, might be necessary to fully determine the polynomial's factorization.
Transcribed Image Text:## Problem Statement 16. Find the "complete" factored form, including the leading coefficient, of the 6th-degree polynomial, \( g(x) \), shown in the graph below. ## Graph Analysis The graph depicts a polynomial function with the following characteristics: - **Degree**: 6th degree, as indicated in the problem statement. - **Behavior at Infinity**: The graph rises to positive infinity on both the left and right extremes, indicating a positive leading coefficient. ### Key Features: - **Intercepts**: The graph intersects the x-axis at \( x \approx -6, -3, \) and \( 1 \). - **Turning Points**: The polynomial has several turning points, consistent with it being a 6th-degree polynomial. ### End Behavior: - As \( x \to -\infty \), \( g(x) \to \infty \) - As \( x \to \infty \), \( g(x) \to \infty \) ## Conclusion To find the complete factored form of the polynomial, consider the x-intercepts and the behavior of the graph. Note that further analysis, such as determining multiplicities and verifying with algebraic methods or technology, might be necessary to fully determine the polynomial's factorization.
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