Question

Factorise:
$6{(2x-\frac{3}{x})}^2-2(2x-\frac{3}{x})-20$

Answer 1

$6(2x-\frac{3}{x}{)}^2-2(2x-\frac{3}{x})-20Put(2x-\frac{3}{x})=vEquationbecomes6v^2-2v-20\Rightarrow 6v^2-12v+10v-20\Rightarrow 3v(2v-4)+5(2v-4)\Rightarrow (3v+5\left)\right(2v-5)Putthevalueback\Rightarrow (3(2x-\frac{3}{x})+5\left)\right(2(2x-\frac{3}{x})-5)\Rightarrow (6x-\frac{9}{x}+5\left)\right(4x-\frac{6}{x}-5)$