Chapter 8.2, Problem 26E

What is the general form of the particular solution guaranteed to exist by Theorem 6 of the linear nonhomogeneous recurrence relation $a_n=6a_{n-1}-12a_{n-2}+8a_{n-3}+F\left(n\right)$ if

a) $F\left(n\right)=n^2$ ?

b) $F\left(n\right)=2^n$ ?

c) $F\left(n\right)=n{2}^n$ ?

d) $F\left(n\right)={\left(-2\right)}^n$ ?

e) $F\left(n\right)=n^2{2}^n$ ?

f) $F\left(n\right)=n^3{\left(-2\right)}^n$ ?

g) $F\left(n\right)=3$ ?