Đáp án:
$\begin{array}{l}
{x^4} - x - 14 = {x^4} - 2{x^3} + 2{x^3} - 4{x^2} + 4{x^2} - 8x + 7x - 14\\
= {x^3}\left( {x - 2} \right) - 2{x^2}\left( {x - 2} \right) + 4x\left( {x - 2} \right) + 7\left( {x - 2} \right)\\
= \left( {x - 2} \right)\left( {{x^3} - 2{x^2} + 4x + 7} \right)\\
\\
{x^{11}} + {x^{10}} + ... + {x^2} + x + 1\\
= \left( {{x^{11}} + {x^{10}}} \right) + \left( {{x^9} + {x^8}} \right) + \left( {{x^7} + {x^6}} \right) + \left( {{x^5} + {x^4}} \right) + \left( {{x^3} + {x^2}} \right) + \left( {x + 1} \right)\\
= \left( {x + 1} \right)\left( {{x^{10}} + {x^8} + {x^6} + {x^4} + {x^2} + 1} \right)\\
= \left( {x + 1} \right)\left( {{x^2} + 1} \right)\left( {{x^8} + {x^4} + 1} \right)
\end{array}$
