Apply synthetic division to find the quotient and remainder when $2x^3 + 3x^2 + x + 8$ is divided by $x + 2$. Write the dividend with decreasing powers of $x$ and extract the coefficients as the first row: $2$, $3$, $1$, and $8$. Since the divisor is $x + 2$, write it in the form $x - c$ to identify $c = -2$, and place $-2$ in the divisor box. Bring down the first coefficient, $2$, to the third row. Multiply it by the divisor $-2$ to obtain $-4$, and place this in the second row under the second coefficient $3$. Add the column ($3 + (-4)$) to yield $-1$ in the third row. Multiply $-1$ by $-2$ to get $2$, placing it under the third coefficient $1$. Add the column ($1 + 2$) to get $3$. Multiply $3$ by $-2$ to get $-6$, placing it under the fourth coefficient $8$. Add the final column ($8 + (-6)$) to get $2$. The numbers in the third row are $2$, $-1$, $3$, and $2$. The first three form the quotient $2x^2 - x + 3$, and the last number, $2$, is the remainder.