So I have been trying to make a program to factor any polynomial expression by inputting a string. When making the code to check to see if I can factor out an X, I got stuck when I realized there must be a way to individually change one letter of a string. Is this possible?

Yes; the option I can think of right now is to cut the string into two pieces using substrings, add in the character, and reassemble the string, as in this pseudocode:
TI-83 series - :sub(string,1,position-1)+yourstring+sub(string,position+1,length(string)-position
TI-89 series - :left(string,position-1)&yourstring&right(string,position+1)

This will error out if the position is 1 or length(string); it only works for characters that are not the first or last.

im on ti 84.
Thanks, I prob coulda thought of that given enough time

The TI-84 Plus series is a member of the TI-83 series, and thus the above code will work.

IK that.

It's worth mentioning that that method will not work properly on the very first or very last character in a string. Often people will write special cases for those, or pad strings on both ends and later remove the padding.