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^2x+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^22)+(2x+1)
or
T(x) = [S(x)(2x+1)]/(x^22)
Then for each zn is must be R(zn)=(2zn2)/(zn^22)
Which gives another way of rewriting R(zn) but is more complicated.

Posted by Jer
on 20160305 12:02:16 