Write a polynomial f (x) that meets the given conditions.
-Polynomial of lowest degree with zeros of $- 2$ (multiplicity 2 ) and 3 (multiplicity 2 ) and with $f ( 0 ) = - 108$
A) $f ( x ) = - 3 x ^ { 4 } + 6 x ^ { 3 } + 33 x ^ { 2 } - 36 x - 108$
B) $f ( x ) = - 3 x ^ { 4 } + 6 x ^ { 3 } - 111 x ^ { 2 } - 36 x - 108$
C) $f ( x ) = - 3 x ^ { 4 } + 6 x ^ { 3 } + 33 x ^ { 2 } - 18 x - 108$
D) $f ( x ) = x ^ { 4 } - 2 x ^ { 3 } - 11 x ^ { 2 } + 12 x - 108$

Question

Quizplus · Accepted Answer

Given the zeros and their multiplicities, the polynomial can be constructed as $f(x) = a(x + 2)^2(x - 3)^2$. To find the coefficient $a$, we use the condition $f(0) = -108$, which leads to $a = -3$, resulting in the polynomial $f(x) = -3(x + 2)^2(x - 3)^2$, which simplifies to the polynomial in option A.

Write a Polynomial F (X) That Meets the Given Conditions −2- 2−2

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