Chọn câu sai. A. (x – 1)3 + 2(x – 1)2 = (x – 1)2(x + 1

* Hướng dẫn giải

Ta có

$$\begin{gathered} +) {(x – 1)}^3 + 2{(x – 1)}^2 \\ = {(x – 1)}^2(x – 1) + 2{(x – 1)}^2 \\ = {(x – 1)}^2(x – 1 + 2) \\ = {(x – 1)}^2(x + 1) \end{gathered}$$

nên A đúng

$$\begin{gathered} +) {(x – 1)}^3 + 2(x – 1) \\ = (x – 1).{(x – 1)}^2 + 2(x – 1) \\ = (x – 1\left)\right[{(x – 1)}^2 + 2] \end{gathered}$$

nên B đúng

$$\begin{gathered} +) {(x – 1)}^3 + 2{(x – 1)}^2 \\ = (x – 1){(x – 1)}^2 + 2(x – 1\left)\right(x – 1) \\ = (x – 1\left)\right[{(x – 1)}^2 + 2(x – 1)] \\ = (x – 1\left)\right[{(x – 1)}^2 + 2x – 2] \end{gathered}$$

nên C đúng

$$\begin{gathered} +) {(x – 1)}^3 + 2{(x – 1)}^2 \\ = {(x – 1)}^2(x + 1) \ne (x – 1\left)\right(x + 3) \end{gathered}$$

nên D sai

Đáp án cần chọn là: D