Math Is Fun Forum

P(x) is divisible by (x+1) and (x-1) , find P(x) if P(2) = 9.

I determined the answer by trial and error and P(x) turned out to be x^3 + x^2 - x - 1 , but is there any systematic method to apply here if the polynomial was more complex ? How can I really solve this algebraicly ?

TIA