Đáp án:
\[\left( {{x^2} + x + 1} \right).\left( {{x^3} - {x^2} + 1} \right)\]
Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
{x^5} + x + 1\\
= \left( {{x^5} - {x^2}} \right) + \left( {{x^2} + x + 1} \right)\\
= {x^2}.\left( {{x^3} - 1} \right) + \left( {{x^2} + x + 1} \right)\\
= {x^2}.\left( {{x^3} - {1^3}} \right) + \left( {{x^2} + x + 1} \right)\\
= {x^2}.\left( {x - 1} \right).\left( {{x^2} + x.1 + {1^2}} \right) + \left( {{x^2} + x + 1} \right)\\
= {x^2}\left( {x - 1} \right).\left( {{x^2} + x + 1} \right) + \left( {{x^2} + x + 1} \right)\\
= \left( {{x^2} + x + 1} \right).\left[ {{x^2}.\left( {x - 1} \right) + 1} \right]\\
= \left( {{x^2} + x + 1} \right).\left( {{x^3} - {x^2} + 1} \right)
\end{array}\)
