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March 16th, 2018, 05:54 PM  #1 
Member Joined: Sep 2011 Posts: 97 Thanks: 1  Nonzero Polynomials
Hi all, Can someone advise if part (a) is correct? I am not sure how to do part (b). Thanks 
March 16th, 2018, 06:18 PM  #2 
Senior Member Joined: Sep 2016 From: USA Posts: 444 Thanks: 254 Math Focus: Dynamical systems, analytic function theory, numerics 
Part (a) looks fine. For part (b), you should prove that given any field, $F$, the polynomial ring, $F[x]$ is a euclidean domain. From this is easily follows that a polynomial of degree $n$ over any field has at most $n$ roots in that field. Hence, for part (b) the answer is no. 

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