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. $\left( 2 x ^ { 4 } + 2 x ^ { 2 } + 1 \right) \div ( x + 2 )$

A) Q: $2 x ^ { 3 } - 4 x ^ { 2 } + 10 x - 20$
$\mathrm { R } : 41$
B) $\begin{array} { l } \text { Q: } 2 x ^ { 3 } - 4 x ^ { 2 } - 10 x + 20 \\\text { R: } - 41\end{array}$
C) Q: $2 x ^ { 3 } - 4 x ^ { 2 } + 10 x - 20$
$\mathrm { R } : 0$
D) Q: $2 x ^ { 3 } - 4 x ^ { 2 } - 10 x + 20$
$\mathrm { R } : 0$
E) $\begin{array} { l } \text { Q: } 2 x ^ { 3 } - 4 x ^ { 2 } + 10 x - 20 \\\text { R: } - 41\end{array}$