Answer:
k = - 6
Explanation:
the Remainder theorem states that if a polynomial f(x) is divided by (x + a) , then the remainder is f(- a)
given the polynomial is divided by (x + 2) then the remainder is f(- 2)
f(x) = 3x³ - kx² + 2x + 1 , then
f(- 2) = 3(- 2)³- k(- 2)² + 2(- 2) + 1 = - 3 , that is
3(- 8) - k(4) - 4 + 1 = - 3
divide- 24 - 4k - 3 = - 3
- 27 - 4k = - 3 ( add 27 to both sides )
- 4k = 24 ( divide both sides by - 4 )
k = - 6