Đáp án:
$\begin{array}{l}
a)\\
{x^{23}} + {x^{22}} + {x^{21}} + ... + {x^2} + x + 1\\
= \left( {{x^{23}} + {x^{22}}} \right) + \left( {{x^{21}} + {x^{20}}} \right) + ... + \left( {{x^3} + {x^2}} \right) + x + 1\\
= \left( {x + 1} \right)\left( {{x^{22}} + {x^{20}} + ... + {x^2} + 1} \right)\\
= \left( {x + 1} \right).\left( {{x^{20}}.\left( {{x^2} + 1} \right) + ... + {x^2} + 1} \right)\\
= \left( {x + 1} \right)\left( {{x^2} + 1} \right)\left( {{x^{20}} + {x^{16}} + ... + 1} \right)\\
= \left( {x + 1} \right)\left( {{x^2} + 1} \right).\left( {{x^{16}}.\left( {{x^4} + 1} \right) + {x^8}\left( {{x^4} + 1} \right) + {x^4} + 1} \right)\\
= \left( {x + 1} \right)\left( {{x^2} + 1} \right)\left( {{x^4} + 1} \right)\left( {{x^{16}} + {x^8} + 1} \right)\\
A = {2^{10}} - {2^9} - {2^8} - {2^7} - ... - {2^2} - 2 - 1\\
= {2^{10}} - 1 - \left( {{2^9} + {2^8} + {2^7} + ... + {2^2} + 2} \right)\\
= \left( {2 - 1} \right).\left( {{2^9} + {2^8} + {2^7} + ... + 2 + 1} \right)\\
- \left( {{2^9} + {2^8} + {2^7} + ... + {2^2} + 2} \right)\\
= \left( {{2^9} + {2^8} + {2^7} + ... + {2^2} + 2 + 1} \right)\\
- \left( {{2^9} + {2^8} + {2^7} + ... + {2^2} + 2} \right)\\
= 1
\end{array}$
