Write the Function as a Product of Linear and Irreducible $$f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 36 x ^ { 2 } - 12 x + 35$$

Multiple Choice

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients.
- $$f ( x ) = x ^ { 4 } - 12 x ^ { 3 } + 36 x ^ { 2 } - 12 x + 35$$

A) $( x - 7 ) ( x - 5 ) \left( x ^ { 2 } + 1 \right)$
B) $( x - 7 ) ^ { 2 } \left( x ^ { 2 } + 1 \right)$
C) $( x - 7 ) ( x + 5 ) \left( x ^ { 2 } + 1 \right)$
D) $( x + 7 ) ( x - 5 ) \left( x ^ { 2 } + 1 \right)$