An unknown polynomial yields a remainder of 2 upon division by \(x-1\), and a remainder of 1 upon division by \(x-2\). If this polynomial is divided by \((x-1)\)\((x-2)\), then the remainder is.

**Details and assumptions**:

You have to write only the constant if, your answer is \(x+1\) then you have to write only 1.

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