Step-by-step explanation:
[tex]f(x) = { x}^{3} + kx + 16 \\ \\ if \: x + 2\: is \: a \: factor \: of \: f(x) \\ f( - 2) = 0 .....(1)\\ f( - 2) = { (- 2)}^{3} + ( - 2)k + 16 \\ f( - 2)= - 8 - 2k + 16 .......(2)\\ \\ (1) = (2) \\ - 8 - 2k + 16 = 0 \\ - 2k = - 8 \\ k= 4[/tex]
