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March 16th, 2018, 05:54 PM   #1
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Nonzero Polynomials

Hi all,

Can someone advise if part (a) is correct?

I am not sure how to do part (b).

Thanks
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March 16th, 2018, 06:18 PM   #2
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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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