Is my solution for this gcd correct?

[Firepanda]

For the first part of this question:

So if everything was done correctly is -55/16 my answer?

 

[Office_Shredder]

-55/16 is a unit, so that is the same as saying they're co-prime

 

[Mark44]

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.

 

[Firepanda]

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.

 

[Mark44]

I'm still interested in where the -55/16 came from.

 

[Firepanda]

Last remainder of Euclidean division