<s>[INST] $ax^3+8x^2+bx+6$ 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 $x^2-2x-3$.
 [/INST] $$ x^2 - 2 x + 3 = ( x + 1) ( x -3) $$
$ x= -1, x = 3 $ should satisfy the polynomial. So,
$$ -a + 8 -b + 6 =0 ;\,  a \,3^3 + 8 \,3^2 - 3 \,3 + 6 =0 ;$$
Siimplify and solve for $a,b. $
</s>