Phân tích thành nhân tử: x^7 + x^6 - x -1

* Hướng dẫn giải

$\begin{array}{l}{\mathrm{x}}^7+{\mathrm{x}}^6-\mathrm{x}-1={\mathrm{x}}^6\left(\mathrm{x}+1\right)-\left(\mathrm{x}+1\right)=\left(\mathrm{x}+1\right)\left({\mathrm{x}}^6-1\right)\\ =\left(\mathrm{x}+1\right)\left({\mathrm{x}}^3-1\right)\left({\mathrm{x}}^3+1\right)=\left(\mathrm{x}+1\right)\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2+\mathrm{x}+1\right)\left(\mathrm{x}+1\right)\left({\mathrm{x}}^2-\mathrm{x}+1\right)\\ ={\left(\mathrm{x}+1\right)}^2\left(\mathrm{x}-1\right)\left({\mathrm{x}}^2-\mathrm{x}+1\right)\left({\mathrm{x}}^2+\mathrm{x}+1\right)\end{array}$