$ax^3+8x^2+bx+6$ is exactly divisible by $x^2-2x-3$, find the values of $a$ and $b$ Find the values of $a$ and $b$ for which the polynomial $ax^3+8x^2+bx+6$ is divisible by $x^2-2x-3$.

Suppose that $$ax^3+8x^2+bx+6=(x^2-2x-3)(ax-2).$$ And 
$$(x^2-2x-3)(ax-2)=ax^3-(2a+2)x^2+(4-3a)x+6.$$
So clearly $a=-5, b=19$. 
