If $x = \sqrt { 7 } \text { is a root of } x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21 = 0$

Multiple Choice

If $x = \sqrt { 7 } \text { is a root of } x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21 = 0$ , use synthetic division to factor the polynomial completely and list all real solutions of the equation.

A) $( x - 3 ) ( x - \sqrt { 7 } ) ( x + \sqrt { 7 } ) ; 3 , \sqrt { 7 } , - \sqrt { 7 }$
B) $( x + 3 ) ( x + \sqrt { 7 } ) ^ { 2 } ; - 3 , \sqrt { 7 }$
C) $( x + 3 ) ( x - \sqrt { 7 } ) ^ { 2 } ; - 3 , \sqrt { 7 }$
D) $( x + 3 ) ( x + \sqrt { 7 } ) ^ { 2 } ; 3 , - \sqrt { 7 }$
E) $( x + 3 ) ^ { 2 } ( x - \sqrt { 7 } ) ; - 3 , \sqrt { 7 }$