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