Determine the remainder r whenf(x) is divided by x - c over the field F for the given f(x), c, and F, where R denotes the field of real numbers and C the field of complex numbers. f(x) = x5 + x3+ x + 1, c = 1, F = Z3

Determine the remainder r whenf(x) is divided by x - c over the field F for the given f(x), c, and F, where R denotes the field of real numbers and C the field of complex numbers. f(x) = x5 + x3+ x + 1, c = 1, F = Z3

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.3: Factorization In F [x]

Problem 1E

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Question

Determine the remainder r whenf(x) is divided by x - c over the field F for the given f(x), c, and F, where R denotes the field of real numbers and C the field of complex numbers.

f(x) = x⁵ + x³+ x + 1, c = 1, F = Z₃

Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.

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