Unknown polynomial...........

Algebra Level 3

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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