Finding the other factors of the polynomial and $K$ If $(2x-1)$ is a factor of the polynomial $$p(x)=2x^3-5x^2-kx+3,$$ find $k$ and the other two factors of $p(x)$.

by using the long division 
$$\frac{2x^3-5x^2-kx+3}{2x-1}=x^2-2x-\frac{k+2}{2}+\frac{3-\frac{k+2}{2}}{2x-1}$$
the remainder or last term must be zero
or
$$3-\frac{k+2}{2}=0$$
hence $$k=4$$
the other factors 
$$x^2-2x-3=(x-3)(x+1)$$
