### Understanding Polynomial Division#### Statement (a)If we divide the polynomial \( P(x) \) by the factor \( x - c \) and we obtain a remainder of 0, then we know that \( c \) is a **root** of \( P \).#### Statement (b)If we divide the polynomial \( P(x) \) by the factor \( x - c \) and we obtain a remainder of \( k \), then we know that \( P(c) = k \).### Explanation:- **Roots of a Polynomial:** If dividing a polynomial by \( x-c \) results in a remainder of 0, it confirms that \( c \) is a root, meaning that \( P(c) = 0 \).- **Remainder and Polynomial Evaluation:** The remainder obtained when dividing a polynomial \( P(x) \) by \( x-c \) directly gives the value of the polynomial at \( c \), i.e., \( P(c) = k \).

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(a) If we divide the polynomial P(x) by the factor x – c and we obtain a remainder of 0, then we know that c is ---Select--- of P. (b) If we divide the polynomial P(x) by the factor x – c and we obtain a remainder of k, then we know that P(c) = ?♥

(a) If we divide the polynomial P(x) by the factor x – c and we obtain a remainder of 0, then we know that c is ---Select--- of P. (b) If we divide the polynomial P(x) by the factor x – c and we obtain a remainder of k, then we know that P(c) = ?♥

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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