## First solution.

After extracting the common factor $(x-1)$, we get

$$\begin{array}{ll} (x-1)((x-2)(x-3)+(x-2)-1)= & 1 \text { point } \\ (x-1)\left(x^{2}-5 x+6+x-2-1\right)= & \\ (x-1)\left(x^{2}-4 x+3\right)= & 1 \text { point } \\ (x-1)\left(x^{2}-3 x-x+3\right)= & 1 \text { point } \end{array}$$

Further extraction yields

$$(x-1)(x-3)(x-1)=(x-1)^{2}(x-3)$$