Use the Rational Root Theorem and the Factor Theorem to Help

Multiple Choice

Use the rational root theorem and the factor theorem to help solve the equation. Be sure that the number of solutions for the equation agrees with property of number solutions of a polynomial equation, taking into account multiplicity of solutions. $2 x ^ { 4 } + x ^ { 3 } - 16 x ^ { 2 } - 3 x + 30 = 0$

A) $\left\{ - \frac { 5 } { 2 } , 2 , \pm \sqrt { 3 } \right\}$
B) $\left\{ - \frac { 3 } { 2 } , - 2 , \pm \sqrt { 3 } \right\}$
C) $\left\{ - \frac { 5 } { 2 } , - 1 \pm \sqrt { 3 } \right\}$
D) $\left\{ - \frac { 9 } { 2 } , 1 \pm \sqrt { 3 } \right\}$
E) $\left\{ - \frac { 5 } { 2 } , - 2 , \pm \sqrt { 3 } \right\}$