Answer:
-4
The Problem:
Given f(x) equals 3x^3+ kx +16, and x+2 is a factor of f(x), then what is the value of k?
Explanation:
If x+c is a factor of P then P(-c)=0.
So we are given x+2 is a factor of f so f(-2)=0.
This means we have the following equation:
3(-2)^3+ k(-2) +16=0
Let's solve for k:
3(-8)-2k+16=0
-24-2k+16=0
-8-2k=0
-8=2k
-4=k
k=-4