Divide $f(X)=3X^{3}+4X^{2}-6X+9$ by $g(X)=X^{2}+2X-3$, using long division.

Solution. We write the polynomials with terms of highest degree first, then repeatedly cancel off the terms of highest degree.

So here $q(X)=3X-2$ and $r(X)=7X+3.$