By the remainder theorem, the remainder upon dividing [tex]x^3+5x^2+kx-8[/tex] by [tex]x-3[/tex] is given by the value of this expression when x = 3 :
[tex]3^3 + 5\cdot3^2 + 3k - 8 = 1[/tex]
Solve for k :
[tex]27 + 45 + 3k - 8 = 1 \\\\ 3k = -63 \\\\ \boxed{k = -21}[/tex]
