Question

For which value of m, x + 3 is the factor of the polynomial x³ – 2mx + 21?

Answer 1

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.