The unexpected

Algebra Level 5

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

when f(x) f(x) is divided by (xa)(x-a) , the remainder is aa;
when f(x)f(x) is divided by (xb)(x-b) , the remainder is bb; and
when f(x)f(x) is divided by (xc)(x-c) , the remainder is cc.

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

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