Phân tích đa thức thành nhân tử:

a) \[3x\left( {3 - x} \right) - 6\left( {x - 3} \right)\]

\( = 3x\left( {3 - x} \right) + 6\left( {3 - x} \right)\)

\[ = \left( {3 - x} \right)\left( {3x + 6} \right)\]

\[ = 3\left( {3 - x} \right)\left( {x + 2} \right).\]

b) \({\left( {{x^2} + 1} \right)^2} - 4{x^2}\)

\( = {\left( {{x^2} + 1} \right)^2} - {\left( {2x} \right)^2}\)

\( = \left( {{x^2} + 1 - 2x} \right)\left( {{x^2} + 1 + 2x} \right)\)

\( = {\left( {x - 1} \right)^2}{\left( {x + 1} \right)^2}.\)

c) \[{x^5} + {x^3} - {x^2} - 1\]

\( = \left( {{x^5} + {x^3}} \right) - \left( {{x^2} + 1} \right)\)

\( = {x^3}\left( {{x^2} + 1} \right) - \left( {{x^2} + 1} \right)\)

\( = \left( {{x^2} + 1} \right)\left( {{x^3} - 1} \right)\)

\( = \left( {{x^2} + 1} \right)\left( {x - 1} \right)\left( {{x^2} + x + 1} \right).\)