Solve the Polynomial Equation $$3 x ^ { 4 } + 23 x ^ { 3 } + 89 x ^ { 2 } + 167 x + 78 = 0$$

Multiple Choice

Solve the polynomial equation. In order to obtain the first root, use synthetic division to test the possible rational
roots.
- $$3 x ^ { 4 } + 23 x ^ { 3 } + 89 x ^ { 2 } + 167 x + 78 = 0$$

A) $\left\{ - 3 , - \frac { 2 } { 3 } , - 2 + 3 i , - 2 - 3 i \right\}$
B) $\left\{ 3 , + \frac { 2 } { 3 } , - 3 + 2 i , - 3 - 2 i \right\}$
C) $\left\{ - 3 , + \frac { 2 } { 3 } , - 3 + 2 i , - 3 - 2 i \right\}$
D) $\left\{ 3 , - \frac { 2 } { 3 } , - 2 + 3 i , - 2 - 3 i \right\}$