Let F be a field and a(x), b(x) = F[x] not both zero. The greatest common divisor (ged) ofa(x) and b(r) is the monic polynomial of highest degree that divides both a(x) and b(r). Hencefind the gcd of 3x²+x+6 and 0 in Q[r]

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Let F be a field and a(x), b(x) = F[x] not both zero. The greatest common divisor (gcd) of a(x) and b(r) is the monic polynomial of highest degree that divides both a(x) and b(x). Hence find the ged of 3x² + x + 6 and 0 in Q[x]

Let F be a field and a(x), b(x) = F[x] not both zero. The greatest common divisor (gcd) of a(x) and b(r) is the monic polynomial of highest degree that divides both a(x) and b(x). Hence find the ged of 3x² + x + 6 and 0 in Q[x]

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 1E: 1. Find a monic polynomial of least degree over that has the given numbers as zeros, and a monic...

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Question

Let F be a field and a(x), b(x) = F[x] not both zero. The greatest common divisor (ged) of
a(x) and b(r) is the monic polynomial of highest degree that divides both a(x) and b(r). Hence
find the gcd of 3x²+x+6 and 0 in Q[r]

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