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Algebra Level 4

Considering a mysterious polynomial that returns \( 2 \) as a remainder upon division with \( x - 1 \) and \( 1 \) as a remainder upon division with \( x - 2 \), find out the remainder (\(r \)) obtained if this polynomial is divided by \( (x-1)(x-2) \) and then calculate \( r(3) \) as a function of \( x \)

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