Find all complex zeros of the polynomial function, and write the polynomial in completely factored form.
-$$f ( x ) = 3 x ^ { 4 } + 4 x ^ { 3 } + 28 x ^ { 2 } + 36 x + 9$$
A) $f ( x ) = ( 3 x - 1 ) ( x - 1 ) ( x + 3 i ) ( x - 3 i )$
B) $f ( x ) = ( 3 x + 1 ) ( x + 1 ) ( x + 3 ) ( x - 3 )$
C) $f ( x ) = ( 3 x + 1 ) ( x + 1 ) ( x + 3 i ) ( x - 3 i )$
D) $f ( x ) = ( 3 x - 1 ) ( x - 1 ) ( x + 3 ) ( x - 3 )$

Question

Quizplus · Accepted Answer

The polynomial can be factored as $ (3x + 1)(x + 1)(x + 3i)(x - 3i) $, where $ x = -\frac{1}{3}, -1, 3i, -3i $ are the zeros.

Find All Complex Zeros of the Polynomial Function, and Write f(x)=3x4+4x3+28x2+36x+9f ( x ) = 3 x ^ { 4 } + 4 x ^ { 3 } + 28 x ^ { 2 } + 36 x + 9f(x)=3x4+4x3+28x2+36x+9

Find All Complex Zeros of the Polynomial Function, and Write $f ( x ) = 3 x ^ { 4 } + 4 x ^ { 3 } + 28 x ^ { 2 } + 36 x + 9$