a) (6x5y 2 - 9x4y 3 + 15x3y 4 ) : 3x3y 2 b) (2x3 - 21x2 + 67x - 60) : (x - 5) c) (6x3 – 7x2 – x + 2) : (2x + 1) d) (x2 – y 2 + 6x + 9) : (x + y + 3)

Đáp án:

$\begin{array}{l}
a)\left( {6{x^5}{y^2} - 9{x^4}{y^3} + 15{x^3}{y^4}} \right):3{x^3}{y^2}\\
 = 6{x^5}{y^2}:3{x^3}{y^2} - 9{x^4}{y^3}:3{x^3}{y^2} + 15{x^3}{y^4}:3{x^3}{y^2}\\
 = 2{x^2} - 3xy + 5{y^2}\\
b)\\
\left( {2{x^3} - 21{x^2} + 67x - 60} \right):\left( {x - 5} \right)\\
 = \left( {2{x^3} - 10{x^2} - 11{x^2} + 55x + 12x - 60} \right):\left( {x - 5} \right)\\
 = \left( {x - 5} \right)\left( {2{x^2} - 11x + 12} \right):\left( {x - 5} \right)\\
 = 2{x^2} - 11x + 12\\
c)\\
\left( {6{x^3} - 7{x^2} - x + 2} \right):\left( {2x + 1} \right)\\
 = \left( {6{x^3} + 3{x^2} - 10{x^2} - 5x + 4x + 2} \right):\left( {2x + 1} \right)\\
 = \left( {2x + 1} \right)\left( {3{x^2} - 5x + 2} \right):\left( {2x + 1} \right)\\
 = 3{x^2} - 5x + 2\\
d)\\
\left( {{x^2} - {y^2} + 6x + 9} \right):\left( {x + y + 3} \right)\\
 = \left[ {{{\left( {x + 3} \right)}^2} - {y^2}} \right]:\left( {x + y + 3} \right)\\
 = \left( {x + y + 3} \right)\left( {x - y + 3} \right):\left( {x + y + 3} \right)\\
 = x - y + 3
\end{array}$