Phân tích các đa thức sau thành nhân tử:\( \eqalig...

Câu hỏi: Phân tích các đa thức sau thành nhân tử:\( \eqalign{& a)\,\,2x - 7\sqrt x - 9\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,d)\,\,3x + 2\sqrt x - 5 \cr & b)\,\,x - 9\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,e)\,\,\,4\sqrt x - x - 4 \cr & c)\,\,x\sqrt x - 1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,f)\,\,x + \sqrt x - 6 \cr} \)

Đáp án

- Hướng dẫn giải

Phương pháp giải:

Giải chi tiết:

\(\eqalign{& a)\,\,2x - 7\sqrt x - 9 = 2x + 2\sqrt x - 9\sqrt x - 9 \cr & = 2\sqrt x \left( {\sqrt x + 1} \right) - 9\left( {\sqrt x + 1} \right) \cr & = \left( {\sqrt x + 1} \right)\left( {2\sqrt x - 9} \right). \cr & b)\,x - 9 = {\left( {\sqrt x } \right)^2} - {3^2} \cr & = \left( {\sqrt x - 3} \right)\left( {\sqrt x + 3} \right). \cr & c)\,\,x\sqrt x - 1 = {\left( {\sqrt x } \right)^3} - 1 \cr & = \left( {\sqrt x - 1} \right)\left( {x + \sqrt x + 1} \right). \cr & \cr} \)

\( \eqalign{& d)\,3x + 2\sqrt x - 5 = 3x - 3\sqrt x + 5\sqrt x - 5 \cr & = 3\sqrt x \left( {\sqrt x - 1} \right) + 5\left( {\sqrt x - 1} \right) \cr & = \left( {\sqrt x - 1} \right)\left( {3\sqrt x + 5} \right). \cr & e)\,4\sqrt x - x - 4 = - \left( {x - 4\sqrt x + 4} \right) \cr & = - {\left( {\sqrt x - 2} \right)^2}. \cr & f)\,x + \sqrt x - 6 = x + 3\sqrt x - 2\sqrt x - 6 \cr & = \sqrt x \left( {\sqrt x + 3} \right) - 2\left( {\sqrt x + 3} \right) \cr & = \left( {\sqrt x + 3} \right)\left( {\sqrt x - 2} \right). \cr} \)

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