Find the division of the following by synthetic division method: $p(t) = 2t^2 + 3t + 1$ by $t + 2$.

(A) To divide $p(t) = 2t^2 + 3t + 1$ by $t + 2$ using synthetic division:
$1$. Identify the root of the divisor $t + 2 = 0$,which is $t = -2$.
$2$. Write the coefficients of the dividend $p(t) = 2t^2 + 3t + 1$,which are $2, 3, 1$.
$3$. Perform synthetic division:
- Bring down the first coefficient: $2$.
- Multiply by the root: $2 \times (-2) = -4$.
- Add to the next coefficient: $3 + (-4) = -1$.
- Multiply by the root: $(-1) \times (-2) = 2$.
- Add to the next coefficient: $1 + 2 = 3$.
$4$. The resulting coefficients are $2$ and $-1$,representing the quotient $2t - 1$.
$5$. The final value $3$ is the remainder.
Quotient polynomial: $2t - 1$;
Remainder polynomial: $3$.