further comments:

1. 3rd question: I'd like to see the reasoning please.
   5th question: We should use (x+1); otherwise the minus sign
   might throw people off when comparing coefficients (it threw me off)

8b. This part is easy to get confused on, and if people make a mistake
    here, then 8c is worthless. It's just as easy to ask them to solve
    a new recurrence in 8c... we could choose simple roots like 1,2 or
    1, -1 and it wouldn't be too difficult.

12b. Al and I made a mistake here; we forgot to square 35. disregard
    my earlier comment please.