A polynomial P(x) is divided by (x-1), and gives a remainder of 1. When P(x) is divided by (x+1), it gives a remainder of 3. Find the remainder when P(x) is divided by (x^2 - 1)
The Attempt at a Solution
I know that
P(x) = (x-1)A(x) + 1
and P(x) = (x+1)B(x) + 3
But how would I relate to (x^2 -1)? I can multiply the two equations together to get (x^2 -1) but things get pretty messy.