Answer: k = 6
Step-by-step explanation
The remainder theorem: If p(x) is divided by x-m, then p(m) is the remainder.
The x+8 is the same as x-(-8) to show m = -8.
Plug this into the function so we can solve for k.
f(x)=2x^2+kx+15
f(-8) = 2(-8)^2 + k(-8) + 15
95 = 2(64) - 8k + 15
95 = 128 - 8k + 15
95 = 143 - 8k
143-8k = 95
-8k = 95-143
-8k = -48
k = -48/(-8)
k = 6
Therefore, the function f(x) = 2x^2+6x+15 divided over (x+8) gives some quotient and a remainder of 95.