If $x = \sqrt { 6 }$ Is a Root Of $x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0$

Multiple Choice

If $x = \sqrt { 6 }$ is a root of $x ^ { 3 } + 5 x ^ { 2 } - 6 x - 30 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

A) $( x + 5 ) ( x - \sqrt { 6 } ) ( x + \sqrt { 6 } ) ; - 5 , \sqrt { 6 } , - \sqrt { 6 }$
B) $( x - 5 ) ( x + \sqrt { 6 } ) ^ { 2 } ; 5 , \sqrt { 6 }$
C) $( x - 5 ) ( x - \sqrt { 6 } ) ^ { 2 } ; 5 , \sqrt { 6 }$
D) $( x - 5 ) ( x + \sqrt { 6 } ) ^ { 2 } ; - 5 , - \sqrt { 6 }$
E) $( x - 5 ) ^ { 2 } ( x - \sqrt { 6 } ) ^ { 2 } ; 5 , \sqrt { 6 }$