Factor F(x) into Linear Factors Given That K Is a Zero

Multiple Choice

Factor f(x) into linear factors given that k is a zero of f(x) .
- $f ( x ) = x ^ { 4 } + 16 x ^ { 3 } + 62 x ^ { 2 } - 32 x - 128 ; k = - 8$ (multiplicity 2 $)$

A) $f ( x ) = ( x + 8 ) ^ { 2 } ( x - 2 ) ( x + 2 )$
B) $f ( x ) = ( x - 8 ) ( x + 8 ) ( x - \sqrt { 2 } ) ( x + \sqrt { 2 } )$
C) $f ( x ) = ( x - 8 ) ^ { 2 } ( x - \sqrt { 2 } ) ( x + \sqrt { 2 } )$
D) $f ( x ) = ( x + 8 ) ^ { 2 } ( x - \sqrt { 2 } ) ( x + \sqrt { 2 } )$