The unexpected

Algebra Level 5

Let $f(x)$ be a polynomial of degree 3 such that

when $f(x)$ is divided by $(x-a)$ , the remainder is $a$ ;
when $f(x)$ is divided by $(x-b)$ , the remainder is $b$ ; and
when $f(x)$ is divided by $(x-c)$ , the remainder is $c$ .

Evaluate the remainder when $f(x)$ is divided by $(x-a)(x-b)(x-c)$ .

a

ab +bc +ca

Depends on the values of

x,a,b

and

c

b

(a+b+c)

c

x