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.
-$$f ( x ) = 3 x ^ { 3 } - x ^ { 2 } + 2 x + 3 ; k = - 1$$
A) $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } + 2 x \right) + 3$
B) $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } - 4 x + 2 \right) + 5$
C) $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } - 4 x + 6 \right) - 3$
D) $f ( x ) = ( x - 1 ) \left( 3 x ^ { 2 } + 2 x \right) + 3$

Question

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The Answer of 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.
-$$f ( x ) = 3 x ^ { 3 } - x ^ { 2 } + 2 x + 3 ; k = - 1$$
A) $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } + 2 x \right) + 3$
B) $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } - 4 x + 2 \right) + 5$
C) $f ( x ) = ( x + 1 ) \left( 3 x ^ { 2 } - 4 x + 6 \right) - 3$
D) $f ( x ) = ( x - 1 ) \left( 3 x ^ { 2 } + 2 x \right) + 3$