Correct. The GCF of the three terms is $\displaystyle{6}{x}\usepackage{cmbright}\Huge\$ . So:

$\displaystyle{6}{{x}}^{{3}}+{18}{{x}}^{{2}}-{240}{x}={6}{x}{\left({{x}}^{{2}}+{3}{x}-{40}\right)}={6}{x}{\left({{x}}^{{2}}-{5}{x}+{8}{x}-{40}\right)}={6}{x}{\left({x}-{5}\right)}{\left({x}+{8}\right)}\usepackage{cmbright}\Huge\$