By definition, if (x + 2) is a factor, then x = -2 is a factor to the polynomial using the Remainder and Factor theorem.
Thus, we can say that the remainder when x = -2 should be 0.
P(-2) = 0;
3(-2)³ +4(-2)² - 2k - 8 = 0
3(-8) + 16 - 2k - 8 = 0
-24 + 16 - 8 - 2k = 0
-16 -2k = 0
-2k = 16
k = -8
Thus, the value for k that will make (x + 2) a factor is k = -8