Question

if f (x) is divided by (x-a)(x-b) then remainder "r" is?

Answer 1

If P(x) is divided by (x-a)(x-b), where a is not equal to b and a and b are elements of the real number set, prove that the remainder is

[(P(b)-P(a))/(b-a)] x (x-a) + P(a)

I was able to make some progress, but I am not able to fully prove this problem. Any help would be appreciated.