We have
Let
Thus
Hence so the remainder when is divided by is
Im currently stuck on this question:
When P(z) is divided by z+1 the remainder is -8 and when divided by z-3 the remainder is 4. Find the remainder when P(z) is divided by (z-3)(z+1)
I know that P(-1) = -8 and P(3) = 4 but i have no clue what to do from here.
Thanks for any help
I am basically using the result that given any polynomials with there exist polynomials with either or such that (This applies to polynomials over a field such as the field of rationals, reals or complex numbers.) The polynomial is the remainder when is divided by
Actually, I didn’t do a great job in my post above. Let me re-do the proof in a clearer way.
Given polynomials and we have that there exist a polynomial and constants such that
As and we have and Solving the two simultaneous equations should yield Hence the remainder is