# Does this REMIND you of something else ?

**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 \( x \)