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

* Hướng dẫn giải

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

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