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

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

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

Answer»

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.