Answer:
k = 14
Explanation:
The Remainder theorem states that if f(x) is divided by (x + h) then the remainder is f(- h)
If (x + h) is a factor of f(x) then the remainder is zero, that is f(- h) = 0
Given (x + 2) is a factor of f(x) then f(- 2) = 0, that is
(- 2)³ + 8(- 2)² - 2k + 4 = 0
- 8 + 8(4) - 2k + 4 = 0
- 8 + 32 - 2k + 4 = 0
- 2k + 28 = 0 ( subtract 28 from both sides )
- 2k = - 28 ( divide both sides by - 2 )
k = 14