Apply synthetic division to find the quotient and remainder when $3x^3 + 10x^2 + 6x - 2$ is divided by $x + 2$. Write the coefficients of the dividend in the first row: $3$, $10$, $6$, and $-2$. The divisor is $x + 2$, so place $c = -2$ in the divisor box. Bring down the first coefficient, $3$, to the third row. Multiply $3$ by $-2$ to get $-6$, and place it in the second row under the second coefficient $10$. Add the column ($10 + (-6)$) to get $4$ in the third row. Multiply $4$ by $-2$ to get $-8$, placing it under $6$. Add the column ($6 + (-8)$) to get $-2$. Multiply $-2$ by $-2$ to get $4$, placing it under the final coefficient $-2$. Add the column ($-2 + 4$) to get $2$. The third row numbers are $3$, $4$, $-2$, and $2$. The first three numbers give the quotient $3x^2 + 4x - 2$, and the final number $2$ is the remainder.