let p(x) = x ³ – 2mx² + 16, and g(x) = x + 2

Putting g(x) = 0 ⟹ x + 2 = 0 ⟹ x = – 2

According to factor theorem if p(x) is divisible by g(x), the remainder p(−2) should be zero.

p( – 2) = 0 ⟹ ( – 2)³ – 2m( – 2)² + 16 =0 – 8 – 8m + 16 = 0

⟹ 8m = 8 ⟹ m = 1