Given f(x) equals 3x^3+ kx +16, and x+2 is a factor of f(x), then what is the value of k?

-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?

Step-by-step 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

wheres graph

step-by-step explanation: