Answered: 6. Let P be a non-zero polynomial such…

6. Let P be a non-zero polynomial such that P(1 + x) = P(1 – x) for all real x and P(1) = 0. Let m be the largest integer such that (x – 1)" divides P(x) for all such P(x). Then, m equals %3D

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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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Question

6. Let P be a non-zero polynomial such that
P(1+ x) = P(1 – x) for all real x and P(1) =0. Let m be
the largest integer such that (x – 1)" divides P(x) for
all such P(x). Then, m equals
%3D
%3D
(a) 1
^(c) 3
(b) 2
(d) 4

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