1. Mar 20, 2010 #1

   Firepanda

   

   For the first part of this question:
   
   
   
   So if everything was done correctly is -55/16 my answer?

    

   Last edited: Mar 21, 2010

   Firepanda, Mar 20, 2010
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3. Mar 20, 2010 #2

   Office_Shredder

   

   Staff Emeritus

   Science Advisor

   Gold Member

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

    

   Office_Shredder, Mar 20, 2010
4. Mar 21, 2010 #3

   Mark44

   

   Insights Author

   Staff: Mentor

   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.

    

   Mark44, Mar 21, 2010
5. Mar 21, 2010 #4

   Firepanda

   

   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.

    

   Last edited: Mar 21, 2010

   Firepanda, Mar 21, 2010
6. Mar 21, 2010 #5

   Mark44

   

   Insights Author

   Staff: Mentor

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

    

   Mark44, Mar 21, 2010
7. Mar 21, 2010 #6

   Firepanda

   

   Last remainder of Euclidean division

    

   Firepanda, Mar 21, 2010

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