Express F(x) in the Form F(x) = (X - K)q(x) $$f ( x ) = 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 ; \quad k = 2$$

Multiple Choice

Express f(x) in the form f(x) = (x - k) q(x) + r for the given value of k.
- $$f ( x ) = 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 ; \quad k = 2$$

A) $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 4 \right) + 7$
B) $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } - 2 x + 11 \right) + 22$
C) $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } + 4 x ^ { 2 } + 2 x + 4 \right) + 22$
D) $f ( x ) = ( x - 2 ) \left( 3 x ^ { 3 } - 4 x ^ { 2 } - 2 x - 4 \right) + 7$