Q. 5

# If p(x) = x^{3} + x^{2} + ax + 115 is exactly divisible by (x + 5) then a = ?

A. 8

B. 6

C. 5

D. 3

Answer :

Given, p(x) = x^{3} + x^{2} + ax + 115

(x^{3} + x^{2} + ax + 115) is exactly divisible by (x + 5)

Hence, substituting x = -5 will give us the value of a

⇒ (-5)^{3} + (-5)^{2} + a (-5) + 115 = 0

⇒ -125 + 25 – 5a + 115 = 0

⇒ 5a = 15

⸫ a = 3

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