Express F(x) in the Form F(x) = (X - K)q(x) $$f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2$$

Express f(x) in the form f(x) = (x - k) q(x) + r for the given value of k.
- $$f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2$$

A) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 6 x ^ { 2 } - 12 \right) + 23$
B) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 8 x \right) - 15$
C) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } + 6 \right) - 13$
D) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 12 \right) - 25$