Question

phân tích đa thức thành nhân tử:5x^2+2x-1

Answer 1

`5x^2+2x-1`

`=(\sqrt{5}x)^2+2.\sqrt{5}x .1/\sqrt{5}+1/5-6/5`

`=(\sqrt{5}x+1/\sqrt{5})^2-(\sqrt{6}/\sqrt{5})^2`

`=(\sqrt{5}x+1/\sqrt{5}-\sqrt{6}/\sqrt{5})(\sqrt{5}x+1/\sqrt{5}+\sqrt{6}/\sqrt{5})`

`=(\sqrt{5}x+[1-\sqrt{6}]/\sqrt{5})(\sqrt{5}x+[1+\sqrt{6}]/\sqrt{5})`

Answer 2

\(5x^2+2x-1=5\left(x^2+\dfrac{2}{5}x-\dfrac{1}{5}\right)=5\left(x^2+2.\dfrac{1}{5}x+\dfrac{1}{25}-\dfrac{6}{25}\right)=5\left[\left(x+\dfrac{1}{5}\right)^2-\dfrac{6}{25}\right]=5\left(x+\dfrac{1-\sqrt{6}}{5}\right)\left(x+\dfrac{1+\sqrt{6}}{5}\right)\)