Using synthetic division ,the     remainder of 3x²-2x+1 is divided by    x-1is

To use synthetic division, follow these steps:

1. Write down the coefficients of the dividend (the polynomial we're dividing), which are 3, -2, and 1.

2. Write down the zero of the divisor (the polynomial we're dividing by). The zero is the solution to the equation x - 1 = 0, which is x = 1.

3. Set up the synthetic division tableau. Draw a line, write the zero on the left, and the coefficients on the right.

4. Bring down the first coefficient (3) to the bottom row.

5. Multiply the number you just wrote down by the zero (1), and write the result (3) under the second coefficient (-2).

6. Add the numbers in this new column (-2 + 3), and write the result (1) in the bottom row.

7. Repeat steps 5 and 6 for the rest of the coefficients. Multiply the number you just wrote down (1) by the zero (1), and write the result (1) under the next coefficient (1). Add the numbers in this column (1 + 1) to get 2.

8. The numbers in the bottom row are the coefficients of the quotient, and the last number is the remainder. So, the quotient is 3x + 1 and the remainder is 2.

Therefore, when 3x² - 2x + 1 is divided by x - 1 using synthetic division, the remainder is 2.