I know how to find the closed form of some recurrence relations such as those that are similar to the Fibonacci Sequence. I am not sure how to solve a recurrence relation using the characteristic polynomial when there is a constant involved like
$a_n = 3a_{n-1} -1$ (I know how to solve this using substitution, but I want to know-how using the characteristic polynomial)
or
$a_n = 6a_{n-1} + 7a_{n-2} +3$
In using the characteristic polynomial, how do I treat the constant when factoring?