Đáp án:
$\begin{array}{l}
a)M = {x^{10}} - 25{x^9} + 25{x^8} - 25{x^7} + ...\\
- 25{x^3} + 25{x^2} - 25x + 25\\
= {x^{10}} - 24{x^9} - {x^9} + 24{x^8} + {x^8} - 24{x^7}\\
- .... - {x^3} + 24{x^2} + {x^2} - 24x - x + 24 + 1\\
= {x^9}\left( {x - 24} \right) - {x^8}\left( {x - 24} \right) + {x^7}\left( {x - 24} \right)\\
- .... - {x^2}\left( {x - 24} \right) + x\left( {x - 24} \right) - \left( {x - 24} \right) + 1\\
= \left( {x - 24} \right)\left( {{x^9} - {x^8} + {x^7} - ... - {x^2} + x - 1} \right) + 1\\
= \left( {24 - 24} \right).\left( {{x^9} - {x^8} + {x^7} - ... - {x^2} + x - 1} \right) + 1\\
= 1\\
b)A = {x^3} - 30{x^2} - 31x + 1\\
= {x^3} - 31{x^2} + {x^2} - 31x + 1\\
= {x^2}\left( {x - 31} \right) + x\left( {x - 31} \right) + 1\\
= \left( {x - 31} \right)\left( {{x^2} + x} \right) + 1\\
= \left( {31 - 31} \right)\left( {{x^2} + x} \right) + 1\\
= 1
\end{array}$
