Use synthetic division to divide \(3x^3 - 2x^2 + 5x - 8\) by \(x - 2\).

Step 1 ：Set up the synthetic division: write the coefficients of the divisor and the dividend in a row, and the zero of the divisor (2 in this case) on the left: \[ \begin{array}{c|cccc} 2 & 3 & -2 & 5 & -8 \ \end{array} \]

Step 2 ：Carry the first coefficient (3) down to the bottom row. Multiply the number brought down by the zero of the divisor (2) and write the result under the next coefficient (-2): \[ \begin{array}{c|ccccc} 2 & 3 & -2 & 5 & -8 \ & & 6 & & \ & 3 & & & \ \end{array} \]

Step 3 ：Add the numbers in the second column to get the next number in the bottom row. Repeat the process for the rest of the columns: \[ \begin{array}{c|ccccc} 2 & 3 & -2 & 5 & -8 \ & & 6 & 12 & 34 \ & 3 & 4 & 17 & 26 \ \end{array} \]

Step 4 ：The numbers in the bottom row are the coefficients of the quotient. The last number is the remainder. So the division gives: \[ 3x^2 + 4x + 17 \text{ remainder } 26 \]