Simplify the Rational Expression $\frac { 4 x ^ { 3 } + x ^ { 2 } - 51 x + 36 } { 4 x - 3 }$

Multiple Choice

Simplify the rational expression, $\frac { 4 x ^ { 3 } + x ^ { 2 } - 51 x + 36 } { 4 x - 3 }$ , by using long division or synthetic division.

A) $x ^ { 2 } + 7 x + 16$
B) $x ^ { 2 } - 7 x - 12$
C) $x ^ { 2 } - 6 x + 12$
D) $x ^ { 2 } + 8 x + 9$
E) $x ^ { 2 } + x - 12$