For the first part of this question:
So if everything was done correctly is -55/16 my answer?
-55/16 is a unit, so that is the same as saying they're co-prime
Maybe I'm missing something, but I don't get where the -55/16 comes from. f(x) has no zeroes in the rationals, hence no factors with rational coefficients.
I'm not sure what F5 means, but if it represents the integers modulo 5, both f and g have a common zero, hence a common factor.
I had my solution steps up last night but I took it down after office_shredder made the point that it means they are coprime.
I'm still interested in where the -55/16 came from.
Last remainder of Euclidean division
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