Polynomial. Again?

Algebra Level 3

Suppose a polynomial \(p(x)\) such that it has a the following properties:
- Leaves a remainder \(a\) on division by \((x-a)\),
- Leaves a remainder \(b\) on division by \((x-b)\),
- Leaves a remainder \(c\) on division by \((x-c)\).

Find the remainder when \(p(x)\) is divided by \((x-a)(x-b)(x-c)\).

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