Using synthetic division ,the     remainder of 3x²-2x+1 is divided by    x-1is*2345

Sure, let's use synthetic division to find the remainder when 3x²-2x+1 is divided by x-1.

Step 1: Write down the coefficients of the dividend (3x²-2x+1), which are 3, -2, and 1.

Step 2: Write down the zero of the divisor (x-1). The zero is the solution to the equation x-1=0, which is x=1.

Step 3: Set up the synthetic division. Draw a line, write the zero (1) to the left of the line, and the coefficients (3, -2, 1) to the right of the line.

Step 4: Bring down the first coefficient (3) below the line.

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

Step 6: Add the numbers in this new column (-2 and 3), and write the result (1) below the line.

Step 7: Repeat steps 5 and 6 with the new number you just wrote down (1). Multiply it by the zero (1), and write the result (1) under the third coefficient (1). Add the numbers in this new column (1 and 1), and write the result (2) below the line.

The number at the bottom right (2) is the remainder when 3x²-2x+1 is divided by x-1. So, the remainder is 2.