Phân tích các đa thức sau thành nhân tử:

a) \[x\left( {x - 3} \right) + 4x - 12\]

\[ = x\left( {x - 3} \right) + \left( {4x - 12} \right)\]

\[ = x\left( {x - 3} \right) + 4\left( {x - 3} \right)\]

\[ = \left( {x - 3} \right)\left( {x + 4} \right)\]

b) \[{x^2} - 2x + 1 - {y^2}\]

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

\[ = {\left( {x - 1} \right)^2} - {y^2}\]

\[ = \left( {x - y - 1} \right)\left( {x + y - 1} \right)\]

c) \[2x - 4 + 5{x^2} - 10x\]

\[ = \left( {2x - 4} \right) + \left( {5{x^2} - 10x} \right)\]

\[ = 2\left( {x - 2} \right) + 5x\left( {x - 2} \right)\]

\[ = \left( {x - 2} \right)\left( {5x + 2} \right)\]

d) \[x\left( {x + 1} \right)\, + \,x\left( {x - 5} \right)\, - \,5\left( {x + 1} \right)\]

\[ = \,\left[ {x\left( {x + 1} \right)\, - \,5\left( {x + 1} \right)} \right]\, + \,x\left( {x - 5} \right)\,\]

\[ = \,\left( {x + 1} \right)\left( {x - 5} \right) + x\left( {x - 5} \right)\]

\[ = \,\left( {x - 5} \right)\left( {x + 1 + x} \right)\]

\[ = \,\left( {x - 5} \right)\left( {2x + 1} \right)\]