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.
-$f ( x ) = - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 ; k = 1$
A) $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1 \right)$
B) $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1 \right)$
C) $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1 \right)$
D) $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9 \right)$

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.
-$f ( x ) = - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 ; k = 1$
A) $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1 \right)$
B) $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1 \right)$
C) $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1 \right)$
D) $f ( x ) = ( x - 1 ) \left( - 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9 \right)$