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

Question

Quizplus · Accepted Answer

The polynomial has real coefficients, so complex roots must occur in conjugate pairs. The zeros are $-4$, $-3 + 2i$, and $-3 - 2i$. The polynomial is $f(x) = a(x + 4)(x + 3 - 2i)(x + 3 + 2i)$. Using the condition $f(-3) = -4$, we find $a = -1$.

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