We can use distribution property to multiply the polynomial by the monomial.
$$ \begin{aligned} \left( 3x-5 \right) \cdot \color{orangered}{x} &= 3x \cdot \color{orangered}{x} + \left( -5\right) \cdot \color{orangered}{x} = \\ &= 3x^2-5x \end{aligned} $$