Đáp án:
$\begin{array}{l}
a)\left( {25{x^5} - 5{x^4} + 10{x^2}} \right):5{x^2}\\
= 5{x^2}.\left( {5{x^3} - {x^2} + 2} \right):5{x^2}\\
= 5{x^3} - {x^2} + 2\\
b)\left( {15{x^3}{y^2} - 6{x^2}y - 3{x^2}{y^2}} \right):6{x^2}y\\
= 15{x^3}{y^2}:6{x^2}y - 6{x^2}y:6{x^2}y - 3{x^2}{y^2}:6{x^2}y\\
= \frac{5}{2}xy - 1 - \frac{1}{2}y\\
c)\left( {6{x^2} + 13x - 5} \right):\left( {2x + 5} \right)\\
= \left( {6{x^2} + 15x - 2x - 5} \right):\left( {2x + 5} \right)\\
= \left( {2x + 5} \right).\left( {3x - 1} \right):\left( {2x + 5} \right)\\
= 3x - 1\\
d)\left( {{x^3} - 3{x^2} + x - 3} \right):\left( {x - 3} \right)\\
= \left( {x - 3} \right)\left( {{x^2} + 1} \right):\left( {x - 3} \right)\\
= {x^2} + 1\\
e)\left( {2{x^4} + {x^3} - 5{x^2} - 3x - 3} \right):\left( {{x^2} - 3} \right)\\
= \left( {2{x^4} - 6{x^2} + {x^3} - 3x + {x^2} - 3} \right):\left( {{x^2} - 3} \right)\\
= \left( {{x^2} - 3} \right)\left( {2{x^2} + x + 1} \right):\left( {{x^2} - 3} \right)\\
= 2{x^2} + x + 1\\
f)\left( {2{x^4} + {x^3} - 3{x^2} + 5x - 2} \right):\left( {{x^2} - x + 1} \right)\\
= \left( \begin{array}{l}
2{x^4} - 2{x^3} + 2{x^2} + 3{x^3} - 3{x^2} + 3x\\
- 2{x^2} + 2x - 2
\end{array} \right):\left( {{x^2} - x + 1} \right)\\
= \left( {{x^2} - x + 1} \right)\left( {2{x^2} + 3x - 2} \right):\left( {{x^2} - x + 1} \right)\\
= 2{x^2} + 3x - 2
\end{array}$
