For what value of m will the expression 3x³ + mx² + 4x – 4m be divisible by x + 2?

Given, f(x) = 3x³ + mx² + 4x – 4m
f(x) is divisible by (x + 2) if f(–2) = 0
Now f(–2) = 3(–2)³ + m(–2)² + 4(–2) – 4m

                   = – 24 + 4m – 8 – 4m = – 32 ≠ 0
No such value of m exists for which (x + 2) is a factor of the given expression.