Advertisements (Quảng cáo)
Bài 79. Phân tích các đa thức sau thành nhân tử:
a) \({x^2} – 4 + {\left( {x – 2} \right)^2}\) ;
b) \({x^3} – 2{x^2} + x – x{y^2}\) ;
c) \({x^3} – 4{x^2} – 12x + 27\).
Hướng dẫn làm bài:
a) \({x^2} – 4 + {\left( {x – 2} \right)^2}\)
= \(\left( {{x^2} – {2^2}} \right) + {\left( {x – 2} \right)^2}\)
=\(\left( {x – 2} \right)\left( {x + 2} \right) + {\left( {x – 2} \right)^2}\)
=\(\left( {x – 2} \right)\left[ {\left( {x + 2} \right) + \left( {x – 2} \right)} \right]\)
=\(\left( {x – 2} \right)\left( {x + 2 + x – 2} \right)\)
=\(\left( {x – 2} \right)\left( {2x} \right)\)
=\(2x\left( {x – 2} \right)\)
Advertisements (Quảng cáo)
b) \({x^3} – 2{x^2} + x – x{y^2}\)
=\(x\left( {{x^2} – 2x + 1 – {y^2}} \right)\)
=\(x\left[ {{{\left( {x – 1} \right)}^2} – {y^2}} \right]\)
=\(x\left( {x – 1 – y} \right)\left( {x – 1 + y} \right)\)
c) \({x^3} – 4{x^2} – 12x + 27\)
= \(\left( {{x^3} + 27} \right) – \left( {4{x^2} + 12x} \right)\)
=\(\left( {x + 3} \right)\left( {{x^2} – 3x + 9} \right) – 4x\left( {x + 3} \right)\)
=\(\left( {x + 3} \right)\left( {{x^2} – 3x + 9 – 4x} \right)\)
=\(\left( {x + 3} \right)\left( {{x^2} – 7x + 9} \right)\)