Let E be a field and , 6E Ebe nonzero polynomials.(a) If ab and a, prove that a = db for some nonzero d E E(b) If e gcd(a, b) andE Eis a common divisor of a and b of highest possible degree, prove thati= de for some nonzero d E E

Let E be a field and a, b ∈ E[x] be non-zero polynomials.

Answered: Let E be a field and , 6E E be nonzero…

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 10E

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Let E be a field and , 6E E be nonzero polynomials. (a) If ab and a, prove that a = db for some nonzero d E E (b) If e gcd(a, b) and E Eis a common divisor of a and b of highest possible degree, prove that i= de for some nonzero d E E