Question

factorise 2(5x-1/x)^2- 3(5x-1/x) - 2

Answer 1

$Let\: (5x-\frac{1}{x})\: be\: \omega, \\ 2\omega^{2}-3\omega-2\\=2\omega^{2}-(4-1)\omega-2\\=2\omega^{2}-4\omega+ \omega-2\\= 2\omega(\omega-2)+1(\omega-2)\\ (2\omega+1)(\omega-1)\\ =(2\times (5x-\frac{1}{x})+1)(5x-\frac{1}{x}-1) \\ =(\frac{10x^{2}-2+x}{x})(\frac{5x^{2}-1-x}{x})$