Yeah you made some errors, you did 2 + 2 + 2 = 8, where its supposed to be 6, and thus parts c and d are incorrect, but i see how you do it now.
All you have to do for part d, is use
A^3+A^2+2=0
but multiply both sides by A. To solve A^4 + B^4.......i cant be bothered... right?