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 \( (x-a)(x-b)(x-c) \).
by
Yash Mehan