Đáp án:

25) \(\left( {5x - 2} \right)\left( {{x^2} - 2x + 5} \right)\)

Giải thích các bước giải:

\(\begin{array}{l}
13) - 2{x^4} + 2{x^3} - 9{x^3} + 9{x^2} - 10{x^2} + 10x - 3x + 3\\
 =  - 2{x^3}\left( {x - 1} \right) - 9{x^2}\left( {x - 1} \right) - 10x\left( {x - 1} \right) - 3\left( {x - 1} \right)\\
 = \left( {x - 1} \right)\left( { - 2{x^3} - 9{x^2} - 10x - 3} \right)\\
 = \left( {x - 1} \right)\left( { - 2{x^3} - 6{x^2} - 3{x^2} - 9x - x - 3} \right)\\
 = \left( {x - 1} \right)\left( { - 2{x^2}\left( {x + 3} \right) - 3x\left( {x + 3} \right) - \left( {x + 3} \right)} \right)\\
 = \left( {x - 1} \right)\left( {x + 3} \right)\left( { - 2{x^2} - 3x - 1} \right)\\
 = \left( {x - 1} \right)\left( {x + 3} \right)\left( { - 2{x^2} - 2x - x - 1} \right)\\
 = \left( {x - 1} \right)\left( {x + 3} \right)\left( { - 2x\left( {x + 1} \right) - \left( {x + 1} \right)} \right)\\
 = \left( {x - 1} \right)\left( {x + 3} \right)\left( {x + 1} \right)\left( { - 2x - 1} \right)\\
15){x^5} - {x^4} - 4{x^4} + 4{x^3} + 2{x^3} - 2{x^2} + {x^2} - x + 6x - 6\\
 = {x^4}\left( {x - 1} \right) - 4{x^3}\left( {x - 1} \right) + 2{x^2}\left( {x - 1} \right) + x\left( {x - 1} \right) + 6\left( {x - 1} \right)\\
 = \left( {x - 1} \right)\left( {{x^4} - 4{x^3} + 2{x^2} + x + 6} \right)\\
 = \left( {x - 1} \right)\left( {{x^4} - 2{x^3} - 2{x^3} + 4{x^2} - 2{x^2} + 4x - 3x + 6} \right)\\
 = \left( {x - 1} \right)\left( {{x^3}\left( {x - 2} \right) - 2{x^2}\left( {x - 2} \right) - 2x\left( {x - 2} \right) - 3\left( {x - 2} \right)} \right)\\
 = \left( {x - 1} \right)\left( {x - 2} \right)\left( {{x^3} - 2{x^2} - 2x - 3} \right)\\
 = \left( {x - 1} \right)\left( {x - 2} \right)\left( {{x^3} - 3{x^2} + {x^2} - 3x + x - 3} \right)\\
 = \left( {x - 1} \right)\left( {x - 3} \right)\left( {x - 3} \right)\left( {{x^2} + x + 1} \right)\\
17)2{x^3} + 3{x^2} + 2{x^2} + 3x + 2x + 3\\
 = {x^2}\left( {2x + 3} \right) + x\left( {2x + 3} \right) + \left( {2x + 3} \right)\\
 = \left( {2x + 3} \right)\left( {{x^2} + x + 1} \right)\\
19)4{x^3} - 3{x^2} + 4{x^2} - 3x + 4x - 3\\
 = {x^2}\left( {4x - 3} \right) + x\left( {4x - 3} \right) + \left( {4x - 3} \right)\\
 = \left( {4x - 3} \right)\left( {{x^2} + x + 1} \right)\\
21)4{x^3} - 3{x^2} - 4{x^2} + 3x - 4x + 3\\
 = {x^2}\left( {4x - 3} \right) - x\left( {4x - 3} \right) - \left( {4x - 3} \right)\\
 = \left( {4x - 3} \right)\left( {{x^2} - x - 1} \right)\\
23)4{x^3} + 3{x^2} - 8{x^2} - 6x + 12x + 9\\
 = {x^2}\left( {4x + 3} \right) - 2x\left( {4x + 3} \right) + 3\left( {4x + 3} \right)\\
 = \left( {4x + 3} \right)\left( {{x^2} - 2x + 3} \right)\\
25)5{x^3} - 2{x^2} - 10{x^2} + 4x + 10x - 4\\
 = {x^2}\left( {5x - 2} \right) - 2x\left( {5x - 2} \right) + 5\left( {5x - 2} \right)\\
 = \left( {5x - 2} \right)\left( {{x^2} - 2x + 5} \right)
\end{array}\)