Giải thích các bước giải:
$\begin{array}{l}
a){x^4} - 5{x^3} + 2{x^2} - x + 3\\
= \left( {{x^4} - {x^3}} \right) - \left( {4{x^3} - 4{x^2}} \right) - \left( {2{x^2} - 2x} \right) - \left( {3x - 3} \right)\\
= \left( {x - 1} \right)\left( {{x^3} - 4{x^2} - 2x - 3} \right)\\
b){x^3} + 3{x^2} - x - 3\\
= \left( {{x^3} + 3{x^2}} \right) - \left( {x + 3} \right)\\
= \left( {x + 3} \right)\left( {{x^2} - 1} \right)\\
= \left( {x + 3} \right)\left( {x - 1} \right)\left( {x + 1} \right)\\
c){x^3} + 2{x^2} + 4x + 3\\
= \left( {{x^3} + {x^2}} \right) + \left( {{x^2} + x} \right) + \left( {3x + 3} \right)\\
= \left( {x + 1} \right)\left( {{x^2} + x + 3} \right)\\
d)6{x^3} - 17{x^2} - 26x - 3\\
= \left( {6{x^3} + 6{x^2}} \right) - \left( {23{x^2} + 23x} \right) - \left( {3x + 3} \right)\\
= \left( {x + 1} \right)\left( {6{x^2} - 23x - 3} \right)\\
e){x^4} - 3{x^3} + 6{x^2} + 13x + 3\\
= \left( {{x^4} + {x^3}} \right) - \left( {4{x^3} + 4{x^2}} \right) + \left( {10{x^2} + 10x} \right) + \left( {3x + 3} \right)\\
= \left( {x + 1} \right)\left( {{x^3} - 4{x^2} + 10x + 3} \right)
\end{array}$
