Divide F(x) by D(x), and Write a Summary Statement in the Form

Multiple Choice

Divide f(x) by d(x) , and write a summary statement in the form indicated.
- $f ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 5 x ^ { 2 } + 2 x + 4 ; d ( x ) = x ^ { 2 } + 1 \quad$ (Write answer in fraction form)

A) $\frac { f ( x ) } { \left( x ^ { 2 } + 1 \right) } = \left( x ^ { 2 } - 2 x + 4 \right) + \frac { - 12 } { \left( x ^ { 2 } + 1 \right) }$
B) $\frac { f ( x ) } { \left( x ^ { 2 } + 1 \right) } = \left( x ^ { 2 } + 2 x + 4 \right)$
C) $\frac { f ( x ) } { \left( x ^ { 2 } + 1 \right) } = \left( x ^ { 2 } + 2 x + 4 \right) + \frac { - 12 } { \left( x ^ { 2 } + 1 \right) }$
D) $\frac { f ( x ) } { \left( x ^ { 2 } + 1 \right) } = \left( x ^ { 2 } - 2 x + 4 \right)$