Sum

For which the value of m, x + 3 is the factor of the polynomial x^{3 }- 2mx + 21 ?

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#### Solution

Let `p(x) =x^3 - 2mx + 21`

(x + 3) is the factor of the polynomial `p(x) = x^3 - 2mx + 21`

∴ p(- 3) = 0

⇒ (-3)^{3} - 2m × (-3) + 21 = 0

⇒ -27 + 6m + 21 = 0

⇒ 6m - 6 = 0

⇒ 6m = 6

⇒ m = 1

Thus, the value of m is 1.

Concept: Value of a Polynomial

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