Not asking for answers- just some explanations-
can someone explain how to do
(3x^5+12x^4+11x^3+2x^2-4x-2)/(3x^2-1)
just review the techniques of long division. You can see all the details if you play around here:
http://calc101.com/webMathematica/long-divide.jsp
It's just like regular numeric long division, as long as you line up the powers of x the way you do columns of digits in big numbers.