Dividing a polynomial

Algebra Level 3

When a polynomial \(P(x)\) of degree \(n > 2\) is divided by \(x-3\), the remainder is 5. When \(P(x)\) is divided by \(x-1\), the remainder is 1. Find the remainder when \(P(x)\) is divided by \(x^2-4x+3\).

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