Phân tích thành nhân tử: 

    a) \({x^2} - 2\).                                            b) \({x^2} - 7\).

    c) \({x^2} + 2\sqrt {15} x + 15\).                                              d) \(4{x^2} - 4\sqrt 3 x + 3\).

a) Ta có \({x^2} - 2 = {x^2} - {\left( {\sqrt 2 } \right)^2} = \left( {x - \sqrt 2 } \right)\left( {x + \sqrt 2 } \right)\).

b) Ta có  \({x^2} - 7 = {x^2} - {\left( {\sqrt 7 } \right)^2} = \left( {x - \sqrt 7 } \right)\left( {x + \sqrt 7 } \right)\).

c) Ta có \({x^2} + 2\sqrt {15} x + 15 = {x^2} + 2.x.\sqrt {15}  + {\left( {\sqrt {15} } \right)^2} = {\left( {x + \sqrt {15} } \right)^2}\).

d) Ta có \(4{x^2} - 4\sqrt 3 x + 3 = {\left( {2x} \right)^2} - 2.2x.\sqrt 3  + {\left( {\sqrt 3 } \right)^2} = {\left( {2x - \sqrt 3 } \right)^2}\).