Question

If f(x) = a(x-b) ÷ a-b + b(x-a) ÷ b-a , find f(a) + f(b) + f(a+b) = ?????​

Answer 1

Step-by-step explanation:

If f(x) is a polynomial of degree n, there must be a polynomial g(x) of degree n−1 and a constant r such that

f(x)=(x−a)g(x)+r.

We say that r is the remainder on dividing f(x) by x−a. By taking x=a in the above,

f(a)=(a−a)g(a)+r=r.