Use Long Division to Divide the First Polynomial Below by the Second

Multiple Choice

Use long division to divide the first polynomial below by the second. $x ^ { 5 } + x ^ { 4 } + 7 x ^ { 3 } + x ^ { 2 } + 6 x - 27,$ $x ^ { 2 } + 6$

A) $x ^ { 3 } + x ^ { 2 } - 5 x + 3 + \frac { 1 } { x ^ { 2 } + 6 }$
B) $x ^ { 3 } + x ^ { 2 } + x - 5 + \frac { 3 } { x ^ { 2 } + 6 }$
C) $x ^ { 3 } + x ^ { 2 } + x + 3 + \frac { 1 } { x ^ { 2 } + 6 }$
D) $x ^ { 3 } + 3 x ^ { 2 } + x + 1 - \frac { 5 } { x ^ { 2 } + 6 }$
E) $x ^ { 3 } - 5 x ^ { 2 } + 3 x + 1 + \frac { 1 } { x ^ { 2 } + 6 }$