Đáp án:
$\begin{array}{l}
{x^5} + 1\\
= {x^5} + {x^4} - {x^4} - {x^3} + {x^3} + {x^2} - {x^2} - x + x + 1\\
= {x^4}\left( {x + 1} \right) - {x^3}\left( {x + 1} \right) + {x^2}\left( {x + 1} \right) - x\left( {x + 1} \right) + \left( {x + 1} \right)\\
= \left( {x + 1} \right)\left( {{x^4} - {x^3} + {x^2} - x + 1} \right)
\end{array}$