A polynomial P(x) has remainder R x
+S on division by (x-a) (x-b). If a is not
equal to b, express the constants R
and S in terms of a, b, P(a), P(b). Find
the remainder when P(x) is divided
by (x-a)^2.
Start off with what you know. Substituting x = a,b you have
Ra+S = P(a)
Rb+S = P(b)
Now just solve for R and S.