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A factor of a polynomial P(x) is x - c. Which must be true of P(x)? A P(c) = 0 BP(-) = 0 C_P(0) = c D P(0) P(0) = -c

A factor of a polynomial P(x) is x - c. Which must be true of P(x)? A P(c) = 0 BP(-) = 0 C_P(0) = c D P(0) P(0) = -c

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 A factor of a polynomial \( P(x) \) is \( x - c \). Which must be true of \( P(x) \)? - **A** \( P(c) = 0 \) - **B** \( P(-c) = 0 \) - **C** \( P(0) = c \) - **D** \( P(0) = -c \) ### Explanation In the context of polynomial functions, if \( x - c \) is a factor of \( P(x) \), then \( c \) is a root of the polynomial. This means that when \( x = c \), the polynomial \( P(x) \) equals zero. Therefore, the correct answer is: - **A** \( P(c) = 0 \) This indicates that substituting \( c \) into the polynomial \( P(x) \) results in zero, confirming that \( c \) is indeed a root of the polynomial.
Transcribed Image Text:### Question A factor of a polynomial \( P(x) \) is \( x - c \). Which must be true of \( P(x) \)? - **A** \( P(c) = 0 \) - **B** \( P(-c) = 0 \) - **C** \( P(0) = c \) - **D** \( P(0) = -c \) ### Explanation In the context of polynomial functions, if \( x - c \) is a factor of \( P(x) \), then \( c \) is a root of the polynomial. This means that when \( x = c \), the polynomial \( P(x) \) equals zero. Therefore, the correct answer is: - **A** \( P(c) = 0 \) This indicates that substituting \( c \) into the polynomial \( P(x) \) results in zero, confirming that \( c \) is indeed a root of the polynomial.
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