H.C.F of \( \left(x^{2}-3 x+2\right) \) and \( \left(x^{2}-4 x+3\right) \) is

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x2 −3x+2=x 2 −2x−x+2 

x(x−2)−1(x−2)=(x−2)(x−1) 

Now 

x2 −4x+3=x 2 −3x−x+3 

x(x−3)−1(x−3)=(x−3)(x−1) 

Thus, the only common factor is (x-1)

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