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.
- $f ( x ) = 3 x ^ { 5 } + 4 x ^ { 4 } + 2 x ^ { 2 } - 1 ; \quad k = - 2$

A) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 6 x ^ { 2 } - 12 \right) + 23$
B) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 12 \right) - 25$
C) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } - 2 x ^ { 3 } + 4 x ^ { 2 } + 6 \right) - 13$
D) $f ( x ) = ( x + 2 ) \left( 3 x ^ { 4 } + 2 x ^ { 3 } + 4 x ^ { 2 } + 8 x \right) - 15$

Correct Answer:

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