Given f(x)=3x^2+9x+k and the remainder when f(x) is divided by x+1 is -14, then what is the value of k?

The value of k is -8.

Step-by-step explanation:

Given;

f(x) = 3x² + 9x + k

factor of the function = x + 1

remainder of the function = -14

let x + 1 = 0

x = -1

f(-1) = 3(-1)² + 9(-1) + k = -14

3(-1)² + 9(-1) + k = -14

3 - 9 + k = -14

-6 + k = -14

k = -14 + 6

k = -8

Therefore, the value of k is -8.