Question

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

Answer 1

Let p(x) = x³ − 2mx + 21 

(x + 3) is the factor of the polynomial p(x) = x³ − 2mx + 21

∴ p (−3) = 0

⇒ (−3)³ − 2m × (−3) + 21 = 0

⇒ −27 + 6m + 21 = 0

⇒ 6m − 6 = 0

⇒ 6m = 6

⇒ m = 1

For the value m = 1, x + 3 is the factor of the polynomial x3 − 2mx + 21.