The given expression can be expressed in the trinomial in standard form as,
[tex]\begin{gathered} (2x-1)(x+5)-\frac{1}{2}x^2=\lbrack2x(x+5)-1(x+5)\rbrack-\frac{1}{2}x^2 \\ =\lbrack2x^2+10x-x-5\rbrack-\frac{1}{2}x^2 \\ =\lbrack2x^2+9x-5\rbrack-\frac{1}{2}x^2 \\ =\frac{3}{2}x^2+9x-5 \end{gathered}[/tex]Thus, the above expression is the requried trinomial.
