$x^{5}$ + $x^{4}$ + $x^{3}$ + $x^{2}$ + x + 1 = 0
⇔ ($x^{5}$ + $x^{4}$) + ($x^{3}$ + $x^{2}$) + (x + 1) = 0
⇔ $x^{4}$(x + 1) + $x^{2}$(x + 1) + (x + 1) = 0
⇔ (x + 1).($x^{4}$ + $x^{2}$ + 1) = 0
⇒\(\left[ \begin{array}{l}x + 1 = 0\\x^{4} + x^{2} + 1\end{array} \right.\) ⇔ \(\left[ \begin{array}{l}x=-1\\x∈∅\end{array} \right.\)