Answer: k = 14/3
Step-by-step explanation:
If x+2 is a factor of the other polynomial mentioned, then x = -2 is a root of that polynomial.
This means plugging x = -2 into the cubic expression will have it result in zero.
x^3- kx^2 +3x+7k = y
(-2)^3- k*(-2)^2 +3*(-2)+7k = 0
-8 - 4k - 6 + 7k = 0
3k - 14 = 0
3k = 14
k = 14/3