I was unable to finish but I thought I'd share what I started:
Dividing R(x) by S(x)
Gives R(x) = S(x)*(x^2+1) + (x^2-x+1)
Call this remainder T(x).
Then for each zn it must be that R(zn)=T(zn)
[looking at Brian's solution, which I don't fully understand, this substitution may make things simpler.]
It may not be helpful to try going further and divide S(x) by T(x) but this gives S(x) = T(x)*(x^2-2)+(-2x+1)
T(x) = [S(x)-(-2x+1)]/(x^2-2)
Then for each zn is must be R(zn)=(2zn-2)/(zn^2-2)
Which gives another way of rewriting R(zn) but is more complicated.
Posted by Jer
on 2016-03-05 12:02:16