examday

/TMUA

The polynomial $f(x)=x^3+cx^2+dx-6$ satisfies both of the following:

• $(x+2)$ is a factor of $f(x)$;
• $f(x)$ leaves a remainder of 3 when divided by $(x-1)$.

Once $c$ and $d$ are determined, $f(x)$ can be written as $(x+2)q(x)$ for some quadratic $q(x)$. Find the product of the roots of $q(x)=0$.