Write the Function as a Product of Linear and Irreducible $$f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 12 x ^ { 2 } - 24 x + 32$$

Multiple Choice

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients.
- $$f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 12 x ^ { 2 } - 24 x + 32$$

A) $( x - 4 ) ( x - 2 ) \left( x ^ { 2 } + 1 \right)$
B) $( x - 4 ) ( x - 2 ) \left( x ^ { 2 } + 4 \right)$
C) $( x - 4 ) ( x + 2 ) \left( x ^ { 2 } + 4 \right)$
D) $( x + 4 ) ( x - 2 ) \left( x ^ { 2 } + 4 \right)$