Use Synthetic Division to Determine the Quotient and Remainder for the Division

Multiple Choice

Use synthetic division to determine the quotient and remainder for the division problem. $\left( 4 x ^ { 3 } + 4 x ^ { 2 } - 6 x + 1 \right) \div \left( x + \frac { 1 } { 2 } \right)$

A) Q: $4 x ^ { 2 } - 2 x + 7$
R: 0
B) Q: $4 x ^ { 2 } - 2 x + 7$
R: $\frac { 9 } { 2 }$
C) $\begin{array} { l } \mathrm { Q } : 4 x ^ { 2 } + 2 x - 7 \\\mathrm { R } : - \frac { 9 } { 2 }\end{array}$
D) $\begin{array} { l } \mathrm { Q } : 4 x ^ { 2 } - 2 x + 7 \\\mathrm { R } : - \frac { 9 } { 2 }\end{array}$
E) Q: $4 x ^ { 2 } + 2 x - 7$
$\mathrm { R } : \frac { 9 } { 2 }$