# 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 $(x-a)(x-b)(x-c)$.

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