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Which of the following is NOT a factor of the polynomial function graphed? X 2 TV

Which of the following is NOT a factor of the polynomial function graphed? X 2 TV

Algebra and Trigonometry (6th Edition)
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:** Which of the following is NOT a factor of the polynomial function graphed? **Graph Description:** The graph provided shows a polynomial function plotted on an \(xy\)-coordinate plane. The \(x\)-axis ranges from -4 to 4, and the \(y\)-axis ranges from -8 to 8, with grid lines marked at every integer. **Key features of the graph:** 1. The polynomial passes through the \(x\)-axis at three points: \(x = -2\), \(x = 0\), and \(x = 2\). These points are the roots of the polynomial. 2. The polynomial touches the \(y\)-axis at \(y = 0\) (which corresponds to root \(x = 0\)) and turns at this point, indicating it is a root of even multiplicity. **Analysis:** To determine a factor that is NOT part of this polynomial function, observe the roots of the polynomial. The polynomial's factors can be derived based on these roots. Given that the roots are based on where it crosses the \(x\)-axis (\(x = -2\), \(x = 0\), and \(x = 2\)), and the polynomial having an even root at \(x = 0\): 1. The root \(x = -2\) indicates a factor of \((x + 2)\). 2. The root \(x = 0\) indicates a factor of \(x\), remembering it may appear with a squared term if it is a double root. 3. The root \(x = 2\) indicates a factor of \((x - 2)\). Analyze these elements to identify which factor is NOT present.
Transcribed Image Text:**Question:** Which of the following is NOT a factor of the polynomial function graphed? **Graph Description:** The graph provided shows a polynomial function plotted on an \(xy\)-coordinate plane. The \(x\)-axis ranges from -4 to 4, and the \(y\)-axis ranges from -8 to 8, with grid lines marked at every integer. **Key features of the graph:** 1. The polynomial passes through the \(x\)-axis at three points: \(x = -2\), \(x = 0\), and \(x = 2\). These points are the roots of the polynomial. 2. The polynomial touches the \(y\)-axis at \(y = 0\) (which corresponds to root \(x = 0\)) and turns at this point, indicating it is a root of even multiplicity. **Analysis:** To determine a factor that is NOT part of this polynomial function, observe the roots of the polynomial. The polynomial's factors can be derived based on these roots. Given that the roots are based on where it crosses the \(x\)-axis (\(x = -2\), \(x = 0\), and \(x = 2\)), and the polynomial having an even root at \(x = 0\): 1. The root \(x = -2\) indicates a factor of \((x + 2)\). 2. The root \(x = 0\) indicates a factor of \(x\), remembering it may appear with a squared term if it is a double root. 3. The root \(x = 2\) indicates a factor of \((x - 2)\). Analyze these elements to identify which factor is NOT present.
**Multiple Choice Question: Select the Correct Expression** Choose one of the following mathematical expressions: 1. ( ) \( x + 1 \) 2. ( ) \( x - 8 \) 3. ( ) \( x + 3 \) 4. ( ) \( x - 1 \)
Transcribed Image Text:**Multiple Choice Question: Select the Correct Expression** Choose one of the following mathematical expressions: 1. ( ) \( x + 1 \) 2. ( ) \( x - 8 \) 3. ( ) \( x + 3 \) 4. ( ) \( x - 1 \)
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