[tex]5x^2-18x-8=5x^2-20x+2x-8=5x(x-4)+2(x-4)\\\\=\boxed{(x-4)(5x+2)}\\--------------------------\\5x^2-18x-8=0\\a=5;\ b=-18;\ c=-8\\\\\Delta=b^2-4ac\\\Delta=(-18)^2-4\cdot5\cdot(-8)=324+160=484 \ \textgreater \ 0\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{484}=22\\\\x_1=\dfrac{18-22}{2\cdot5}=\dfrac{-4}{10}=-\dfrac{2}{5}\\\\x_2=\dfrac{18+22}{2\cdot5}=\dfrac{40}{10}=4\\\\5x^2-18x-8=5\left(x+\dfrac{2}{5}\right)(x-4)=(5x+2)(x-4)[/tex]
