This is a trinomial because it has three terms. The terms are $\displaystyle\frac{{1}}{{2}}{{x}}^{{2}}\usepackage{cmbright}\Huge\$ , $\displaystyle{4}{x}\usepackage{cmbright}\Huge\$ , and 2. A binomial has two terms. The correct answer is $\displaystyle-\frac{{2}}{{3}}{{x}}^{{3}}+{5}{x}\usepackage{cmbright}\Huge\$ .