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

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.
- $$f ( x ) = - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 ; \quad k = 2$$

A) $f ( x ) = ( x + 2 ) \left( - 6 x ^ { 2 } + 10 x + 25 \right) - 40$
B) $f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } - 10 x + 15 \right) - 40$
C) $f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } + 10 x + 25 \right) - 40$
D) $f ( x ) = ( x - 2 ) \left( - 6 x ^ { 2 } - 10 x - 15 \right) - 40$

Correct Answer:

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