Recall that two polynomials f (x) and g(x) from F[x] are said to berelatively prime if there is no polynomial of positive degree in F[x]that divides both f (x) and g(x). Show that if f (x) and g(x) are relativelyprime in F[x], they are relatively prime in K[x], where K isany extension of F.

Recall that two polynomials f (x) and g(x) from F[x] are said to berelatively prime if there is no polynomial of positive degree in F[x]that divides both f (x) and g(x). Show that if f (x) and g(x) are relativelyprime in F[x], they are relatively prime in K[x], where K isany extension of F.

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 16E

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Question

Recall that two polynomials f (x) and g(x) from F[x] are said to be
relatively prime if there is no polynomial of positive degree in F[x]
that divides both f (x) and g(x). Show that if f (x) and g(x) are relatively
prime in F[x], they are relatively prime in K[x], where K is
any extension of F.

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