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.
- $$f ( x ) = 3 x ^ { 4 } - 9 x ^ { 3 } + 2 x ^ { 2 } - 6 x ; \quad k = 3$$

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