Đáp án:
$\begin{array}{l}
34)\\
a){x^4} + 2{x^3} + {x^2}\\
= {x^2}\left( {{x^2} + 2x + 1} \right)\\
= {x^2}{\left( {x + 1} \right)^2}\\
b){x^3} - x + 3{x^2}y + 3x{y^2} + {y^3} - y\\
= {x^3} + 3{x^2}y + 3x{y^2} + {y^3} - \left( {x + y} \right)\\
= {\left( {x + y} \right)^3} - \left( {x + y} \right)\\
= \left( {x + y} \right)\left( {{{\left( {x + y} \right)}^2} - 1} \right)\\
= \left( {x + y} \right)\left( {x + y + 1} \right)\left( {x + y - 1} \right)\\
c)5{x^2} - 10xy + 5{y^2} - 20{z^2}\\
= 5.\left( {{x^2} - 2xy + {y^2}} \right) - 20{z^2}\\
= 5.{\left( {x - y} \right)^2} - 20{z^2}\\
= 5.\left( {x - y - 2z} \right)\left( {x - y + 2z} \right)\\
35)\\
a){x^2} + 5x - 6\\
= {x^2} + 6x - x - 6\\
= \left( {x + 6} \right)\left( {x - 1} \right)\\
b)5{x^2} + 5xy - x - y\\
= 5x\left( {x + y} \right) - \left( {x + y} \right)\\
= \left( {x + y} \right)\left( {5x - 1} \right)\\
c)7x - 6{x^2} - 2\\
= - 6{x^2} + 3x + 4x - 2\\
= - 3x\left( {2x - 1} \right) + 2\left( {2x - 1} \right)\\
= \left( {2x - 1} \right)\left( {2 - 3x} \right)
\end{array}$
