Find the possible values of a in the cubic equation. Given that $(x-a)$ is a factor of $x^3-ax^2+2x^2-5x-3$, find the possible values of the constant $a$.
I believe you first have to find the $a$ in the cubic equation then the other $a$ in $(x-a)$, but I'm having problems finding the first $a$. So far all I have is:
$x^3-ax^2+2x^2-5x-3=0$
$x^3-2ax^2-5x=3$

Hint: If $x-a$ is a factor, then $a$ is a zero. Hence,
$$a^3-a^3+2a^2-5a-3=0\implies 2a^2-5a-3=0.$$
