Use Synthetic Division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$

Multiple Choice

Use synthetic division $$f ( x ) \text { by } x - k \text { for the given value of } k \text {. Then express } f ( x ) \text { in the form } f ( x ) = ( x - k ) q ( x ) + r$$ for the given value of k.
- $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } - 5 x + 4 ; \quad k = 2$

A) $f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } + 7 x + 9 \right) + 22$
B) $f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } + x - 3 \right) - 2$
C) $f ( x ) = ( x + 2 ) \left( 2 x ^ { 2 } + x + 3 \right) + 10$
D) $f ( x ) = ( x - 2 ) \left( 2 x ^ { 2 } - 7 x + 11 \right) + 18$