Phân tích thành nhân tử x^4 -2x^3 +2x -1

* Hướng dẫn giải

$$\begin{gathered} x^4-2x^3+2x-1 \\ =\left(x^4-1\right)-\left(2x^3-2x\right) \end{gathered}$$

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