If (x + 3) is a factor of the polynomial (x^{3} + 3x^{2} + nx – 12), where n is a constant, find the value of n.
-
A.
-1 -
B.
-2 -
C.
-3 -
D.
-4
Correct Answer: Option D
Explanation
(x + 3 = 0 implies x = -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 + 27 – 3n – 12 = 0 implies -3n = 12)
(n = -4)