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Use the graph and the factor theorem to list the factors of f(x). y = f(x) -10-8-6-4 1000- 800- 600- 400- 200- -200- -400- -600- -800- N. 2 6 8 10 N

Use the graph and the factor theorem to list the factors of f(x). y = f(x) -10-8-6-4 1000- 800- 600- 400- 200- -200- -400- -600- -800- N. 2 6 8 10 N

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Graph Analysis for Factor Theorem** **Objective:** Use the graph and the factor theorem to list the factors of \( f(x) \). **Graph Description:** - The graph represents a function \( y = f(x) \). - The x-axis ranges from -10 to 10, and the y-axis ranges from -1000 to 1000. - The curve is a polynomial appearing to be a fourth-degree polynomial based on its shape and behavior. - The graph intersects the x-axis at three points: \( x = -3 \), \( x = 2 \), and \( x = 4 \). **Factor Theorem Application:** Using the factor theorem, a factor \( (x - c) \) implies that \( c \) is a root of the polynomial. The roots shown on the graph are: - \( x = -3 \) (appears to be a double root, as the graph touches and bounces off the axis at this point), - \( x = 2 \), - \( x = 4 \). **Options for the Factors of \( f(x) \):** A. \((x - 3), (x - 4), (x + 2), (x - 3)\) B. \((x + 3), (x - 4), (x - 2), (x + 3)\) C. \((x + 3), (x + 4), (x - 2), (x + 3)\) D. \((x - 3), (x + 4), (x + 2), (x - 3)\) **Correct Choice:** - Considering the roots: \((x + 3)\) should appear twice, indicating a double root, while the other factors \((x - 2)\) and \((x - 4)\) appear once. - The correct option is not explicitly listed. Adjust options to include the correct factors based on the roots provided by the graph. **Conclusion:** Use the observed roots from the graph to determine the factors of the polynomial \( f(x) \) through the factor theorem.
Transcribed Image Text:**Graph Analysis for Factor Theorem** **Objective:** Use the graph and the factor theorem to list the factors of \( f(x) \). **Graph Description:** - The graph represents a function \( y = f(x) \). - The x-axis ranges from -10 to 10, and the y-axis ranges from -1000 to 1000. - The curve is a polynomial appearing to be a fourth-degree polynomial based on its shape and behavior. - The graph intersects the x-axis at three points: \( x = -3 \), \( x = 2 \), and \( x = 4 \). **Factor Theorem Application:** Using the factor theorem, a factor \( (x - c) \) implies that \( c \) is a root of the polynomial. The roots shown on the graph are: - \( x = -3 \) (appears to be a double root, as the graph touches and bounces off the axis at this point), - \( x = 2 \), - \( x = 4 \). **Options for the Factors of \( f(x) \):** A. \((x - 3), (x - 4), (x + 2), (x - 3)\) B. \((x + 3), (x - 4), (x - 2), (x + 3)\) C. \((x + 3), (x + 4), (x - 2), (x + 3)\) D. \((x - 3), (x + 4), (x + 2), (x - 3)\) **Correct Choice:** - Considering the roots: \((x + 3)\) should appear twice, indicating a double root, while the other factors \((x - 2)\) and \((x - 4)\) appear once. - The correct option is not explicitly listed. Adjust options to include the correct factors based on the roots provided by the graph. **Conclusion:** Use the observed roots from the graph to determine the factors of the polynomial \( f(x) \) through the factor theorem.
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