Here, p(x) = x3 – 2mx + 21
(x + 3) is a factor of x3 – 2mx + 21.
∴ By factor theorem,
Remainder = 0
∴ P(- 3) = 0
p(x) = x3 – 2mx + 21
∴ p(-3) = (-3)3 – 2(m)(-3) + 21
∴ 0 = – 27 + 6m + 21
∴ 6 + 6m = 0
∴ 6m = 6
∴ m = 1
∴ x + 3 is the factor of x3 – 2mx + 21 for m = 1.