$\text { If } x = \sqrt { 3 } \text { is a root of } x ^ { 3 } - x ^ { 2 } - 3 x + 3 = 0$

Multiple Choice

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

A) $( x + 1 ) ( x + \sqrt { 3 } ) ^ { 2 } ; - 1 , \sqrt { 3 }$
B) $( x + 1 ) ^ { 2 } ( x - \sqrt { 3 } ) ; - 1 , \sqrt { 3 }$
C) $( x + 1 ) ( x + \sqrt { 3 } ) ^ { 2 } ; 1 , - \sqrt { 3 }$
D) $( x + 1 ) ( x - \sqrt { 3 } ) ^ { 2 } ; - 1 , \sqrt { 3 }$
E) $( x - 1 ) ( x - \sqrt { 3 } ) ( x + \sqrt { 3 } ) ; 1 , \sqrt { 3 } , - \sqrt { 3 }$