PineappleCAS VS CASYMBA

You can use the Pineapple cas. Just note that it is still highly recommended that you learn to do derivatives on your own.

Unfortunately, this would require a CAS, which none of the 84 series has. You can use PineappleCAS to do it, though.

CASymba (still active, features and bugfixes being added), PineappleCAS (not maintained anymore)

I was wondering what programs I could use during the Calculus BC Test and if there were any programs that are prohibited. Specifically, I wanted to know if this was allowed or any other programs similar to this - PineappleCAS

https://github.com/nathanfarlow/PineappleCAS There is PineappleCAS for the Plus CE

CASymba (repo/doc ; download) is a new CE CAS engine alternative (or complement) to the well-known PineappleCAS, and it offers other various features

I mean, you could just do it by hand? for zeros of x = 1, 3, 5, the polynomial is just (x-1)(x-3)(x-5). If you need it graphed, then that can be used directly. If you want the equation, then you'd want to look for a CAS that could do the expansion for you. Perhaps PineappleCAS? (Disclaimer: I haven't used PineappleCAS, so no clue how it is)

Unfortunately, the TI-84 Series does not have a CAS (Computer Algebra System), which is what is needed to simplify radicals. You can download PineappleCAS by Nathan Farlow to add one, but be careful. Using it on a standardized test counts as cheating.

CASymba (still active, features and bugfixes being added), PineappleCAS (not maintained anymore)

What about https://github.com/Hamza-STI/CASYMBA ; I forgot if it has this

Yes CASymba: https://github.com/Hamza-STI/CASYMBA

I suggest you use (when allowed) programs like CASymba since they add features you may find helpful.