Solving a recurrence relation (textbook question) $a_{n+1} - a_n = 3n^2 - n$  ;$a_0=3$
I need help for solving the particular solution.
Based on a chart in my textbook if you get $n^2$ the particular solution would be
$A_2n^2 + A_1n + A_0$ and $n$ has the particular solution of $A_1n+A_0$.
So given $3n^2 - n$, my first thought was that if the equation was $n^2-n$ you can have something like $An^2 + Bn+C - (Bn + C) = An^2$.   
Is this process correct if I simply had $n^2-n$ ? If so how would the $3$ in $3n^2$ affect this step?

hint: $a_n = (a_n-a_{n-1})+(a_{n-1}-a_{n-2})+\cdots +(a_2-a_1)+(a_1-a_0)+a_0$
