Iīm a bit confused. Partially because you speak of division and but the equation looks
y = aX^5+ bX^4 + cX^3 +dX^2 + 1/x. or you mean:
( aX^5+ bX^4 + cX^3 +dX^2)/(x+1) ??
If there is a ramainder that canīt be devided, you donīt devide it, for example say the reminder is the constant 7, gives you
ax^3 + bx^2 + 7/(x+1) <--------the reminder cant be devided.
If you wanīt some more explaining search youtube. Some videos on this topic are great.