By the polynomial remainder theorem, the remainder upon dividing a polynomial [tex]p(x)[/tex] by [tex]x-c[/tex] is the same as the value of [tex]p(c)[/tex].
Here [tex]p(x)=2x^3-3x^2+kx-4[/tex] and [tex]c=3[/tex]. We have
[tex]p(3)=23+3k=-7\implies k=-10[/tex]
