The polynomial -6x^3-55x^2+kx-16 has factors x+8 and 3x+2. Determine the value of k.?

Since x+8 is a factor, then x=-8 is a root.
So, let x=-8 in -6x^3-55x^2+kx-16 = 0 and solve for k. Done!

Note that you don't need the other info of 3x+2.

Done!

x=-8 and k=-58
So
-6x³-55x²-58x-16=0