Write a polynomial f (x) that meets the given conditions. Answers may vary.
-Degree 3 polynomial with zeros $4,5 i$, and $- 5 i$
A) $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 25 x - 100$
B) $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 25 x - 100$
C) $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } + 25 x + 100$
D) $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 25 x + 100$

Question

Quizplus · Accepted Answer

Given the zeros $4, 5i$, and $-5i$, the polynomial can be constructed by multiplying the factors associated with these zeros: $(x-4)(x-5i)(x+5i)$. The product of $(x-5i)(x+5i)$ is $x^2 + 25$, and further multiplying by $(x-4)$ gives a polynomial of the form $x^3 - 4x^2 + 25x - 100$, which matches option B.

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