What should be added to $x^3-2x^2-12x-9$ such that it is completely divisible by $x^2+x-6$? I factorized $x^2+x-6$ as $(x+3)(x-2)$. I am unable to understand how to make use of factor theorem to arrive at the solution of this problem. But by actual division we get that $3x+27$ must be added such that $f(-3)=0$ and $f(2)=0$.
Please give me the solution through factor theorem only.