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 \(c\) \[b\] \[(a+b+c)\] \[c\] \[x\]

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