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If (x + 3) is a factor of the polynomial \(x^{3} + 3x^{2} + ...

If (x + 3) is a factor of the polynomial x3+3x2+nx12, where n is a constant, find the value of n.

A.

-1

B.

-2

C.

-3

D.

-4

Correct answer is D

x+3=0x=3

Using remainder theorem, if x + 3 is a factor, f(-3) = 0.

f(3)=(3)3+3(3)2+n(3)12=0

27+273n12=03n=12

n=4