Tháng Sáu 1, 2023

Phân tích các đa thức sau thành nhân tử: \( \eqalign{& a)\,\,3x – 7\sqrt x + 4 \cr & b)\,x\sqrt x – x – 4 \cr & c)\,3x\sqrt x – 7x + 17\sqrt x – 5 \cr} \) \( \eqalign{& d)\,\,x\sqrt x + 5x + 8\sqrt x + 4 \cr & e)\,\,x – \sqrt x – 2001.2002 \cr & f)\,2x\sqrt x + x – 5\sqrt x – 4 \cr} \)

Phân tích các đa thức sau thành nhân tử:

\( \eqalign{& a)\,\,3x – 7\sqrt x + 4 \cr & b)\,x\sqrt x – x – 4 \cr & c)\,3x\sqrt x – 7x + 17\sqrt x – 5 \cr} \)

\( \eqalign{& d)\,\,x\sqrt x + 5x + 8\sqrt x + 4 \cr & e)\,\,x – \sqrt x – 2001.2002 \cr & f)\,2x\sqrt x + x – 5\sqrt x – 4 \cr} \)

Lời giải chi tiết:

\( \eqalign{& a)\,3x – 7\sqrt x + 4 = 3x – 3\sqrt x – 4\sqrt x + 4 \cr & = 3\sqrt x \left( {\sqrt x – 1} \right) – 4\left( {\sqrt x – 1} \right) \cr & = \left( {\sqrt x – 1} \right)\left( {3\sqrt x – 4} \right). \cr & b)\,x\sqrt x – x – 4 = {\left( {\sqrt x } \right)^3} – x – 8 + 4 \cr & = \left[ {{{\left( {\sqrt x } \right)}^3} – 8} \right] – \left( {x – 4} \right) \cr & = \left( {\sqrt x – 2} \right)\left( {x + 2\sqrt x + 4} \right) – \left( {\sqrt x – 2} \right)\left( {\sqrt x + 2} \right) \cr & = \left( {\sqrt x – 2} \right)\left( {x + \sqrt x + 2} \right). \cr & c)\,3x\sqrt x – 7x + 17\sqrt x – 5 \cr & = 3x\sqrt x – x – 6x + 2\sqrt x + 15\sqrt x – 5 \cr & = x\left( {3\sqrt x – 1} \right) – 2\sqrt x \left( {3\sqrt x – 1} \right) + 5\left( {3\sqrt x – 1} \right) \cr & = \left( {3\sqrt x – 1} \right)\left( {x – 2\sqrt x + 5} \right). \cr} \)

\( \eqalign{& d)\,x\sqrt x + 5x + 8\sqrt x + 4 \cr & = x\sqrt x + x + 4x + 4\sqrt x + 4\sqrt x + 4 \cr & = x\left( {\sqrt x + 1} \right) + 4\sqrt x \left( {\sqrt x + 1} \right) + 4\left( {\sqrt x + 1} \right) \cr & = \left( {\sqrt x + 1} \right)\left( {x + 4\sqrt x + 4} \right) \cr & = \left( {\sqrt x + 1} \right){\left( {\sqrt x + 2} \right)^2}. \cr & e)\,x – \sqrt x – 2001.2002 \cr & = x – \sqrt x – 2001\left( {2001 + 1} \right) \cr & = x – \sqrt x – {2001^2} – 2001 \cr & = \left( {\sqrt x – 2001} \right)\left( {\sqrt x + 2001} \right) – \left( {\sqrt x + 2001} \right) \cr & = \left( {\sqrt x + 2001} \right)\left( {\sqrt x – 2002} \right). \cr & f)\,2x\sqrt x + x – 5\sqrt x – 4 \cr & = 2x\sqrt x + 2x – x – \sqrt x – 4\sqrt x – 4 \cr & = 2x\left( {\sqrt x + 1} \right) – \sqrt x \left( {\sqrt x + 1} \right) – 4\left( {\sqrt x + 1} \right) \cr & = \left( {\sqrt x + 1} \right)\left( {2x – \sqrt x – 4} \right). \cr} \)