Chọn câu sai.

Ta có ${\left( {x - 1} \right)^3} + 2{\left( {x - 1} \right)^2} = {\left( {x - 1} \right)^2}\left( {x - 1} \right) + 2.{\left( {x - 1} \right)^2} = {\left( {x - 1} \right)^2}\left( {x - 1 + 2} \right) = {\left( {x - 1} \right)^2}\left( {x + 1} \right)$ nên A đúng

+) ${\left( {x - 1} \right)^3} + 2\left( {x - 1} \right)$$= \left( {x - 1} \right).{\left( {x - 1} \right)^2} + 2\left( {x - 1} \right)$$= \left( {x - 1} \right)\left[ {{{\left( {x - 1} \right)}^2} + 2} \right]$ nên B đúng

+)  ${\left( {x - 1} \right)^3} + 2{\left( {x - 1} \right)^2}$$= \left( {x - 1} \right){\left( {x - 1} \right)^2} + 2\left( {x - 1} \right)\left( {x - 1} \right)$$= \left( {x - 1} \right)\left[ {{{\left( {x - 1} \right)}^2} + 2\left( {x - 1} \right)} \right]$$=\left( {x - 1} \right)\left[ {{{\left( {x - 1} \right)}^2} + 2x - 2} \right]$

nên C đúng.

+) ${\left( {x - 1} \right)^3} + 2{\left( {x - 1} \right)^2}$$= {\left( {x - 1} \right)^2}\left( {x - 1 + 2} \right)$$= {\left( {x - 1} \right)^2}\left( {x + 1} \right)$

$\ne \left( {x - 1} \right)\left( {x + 3} \right)$ 

nên D sai.