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## Homework Statement

Hello guys

So I have the following problem, given the mapping above I have to check weather it's ring homomorphism, and

maybe monomorphism or epimorphism.

## The Attempt at a Solution

So the mapping is obviously well defined, and I have proven it's homomorphism, and it's obviously not monomorphism because a polynomial P(x)= 5 - x

^{2}is in the kernel so kernel is not trivial.

I am not sure how to prove if the function is surjective or not, obviously if the codomain were integers for every integers C , I could just use constant function p(x) = C and function would be surjective.