A polynomial function $f$ has degree 3 , the zeros below, and a solution point of $f ( 1 ) = - 96$. Write $f$ in completely factored form.
$- 2 , - 3 + 4 i$
A) $f ( x ) = ( x + 3 ) ( x + 2 - 4 i ) ( x + 2 + 4 i )$
B) $f ( x ) = - ( x + 2 ) ( x - 4 - 3 i ) ( x - 4 + 3 i )$
C) $f ( x ) = ( x + 2 ) ( x - 4 - 3 i ) ( x - 4 + 3 i )$
D) $f ( x ) = - ( x + 2 ) ( x + 3 - 4 i ) ( x + 3 + 4 i )$
E) $f ( x ) = ( x + 2 ) ( x + 3 - 4 i ) ( x + 3 + 4 i )$

Question

Quizplus · Accepted Answer

The polynomial must include the factors corresponding to the zeros: $x + 2$ and the conjugate pair $x + 3 - 4i$ and $x + 3 + 4i$. The function must also satisfy $f(1) = -96$, which requires a negative leading coefficient.

A Polynomial Function fff Has Degree 3 , the Zeros Below, and a Solution

A Polynomial Function $f$ Has Degree 3 , the Zeros Below, and a Solution