Answer:
k = 5
Explanation:
if (x - a) is a factor of f(x) , then f(a) = 0
given
x - 2 is a factor of f(x) , then f(2) = 0
substitute x = 2 into f(x) , equate to zero and solve for k
f(x) = x³ - kx² + kx + 2 , then
2³ - k(2)² + 2k + 2 = 0 , that is
8 - 4k + 2k + 2 = 0
- 2k + 10 = 0 ( subtract 10 from both sides )
- 2k = - 10 ( divide both sides by - 2 )
k = 5