## Task B-1.2.

Factorize into linear factors $(x-1)(x-2)(x-3)+(x-1)(x-2)+1-x$.
## 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

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