Let f, g = R[x] be polynomials, with deg g > 0. (a) The division rule for polynomials states that ƒ can be divided by g to produce a quotient q and remainder r. Write down the two conclusions that the division rule states about q and r. (b) How do we tell, from q and r, whether g divides f? (c) Suppose that deg f = 8, and (x - 1)³ divides f. What can be said about the multiplicity of x 1 as a solution of f(x) = 0? -

Let f, g = R[x] be polynomials, with deg g > 0. (a) The division rule for polynomials states that ƒ can be divided by g to produce a quotient q and remainder r. Write down the two conclusions that the division rule states about q and r. (b) How do we tell, from q and r, whether g divides f? (c) Suppose that deg f = 8, and (x - 1)³ divides f. What can be said about the multiplicity of x 1 as a solution of f(x) = 0? -

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

Let f, g = R[x] be polynomials, with deg g > 0.
(a) The division rule for polynomials states that ƒ can be divided by g to produce
a quotient q and remainder r. Write down the two conclusions that the division
rule states about q and r.
(b) How do we tell, from q and r, whether g divides f?
(c) Suppose that deg ƒ = 8, and (x − 1)³ divides f. What can be said about the
multiplicity of x 1 as a solution of ƒ(x) = 0?
=

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