Use the method of polynomial division to find the remainder when $3x^4-2x^3+7x^2-5x+1$ is divided by $x^2-3x+1$.

Step 1 ：Step 1: Perform the polynomial division, dividing the first term of the dividend $3x^4$ by the first term of the divisor $x^2$ gives us $3x^2$.

Step 2 ：Step 2: Multiply the divisor $x^2-3x+1$ by $3x^2$ and subtract the result from the dividend. The result is $-11x^3+20x^2-5x+1$.

Step 3 ：Step 3: Repeat the process, dividing the first term of the new dividend $-11x^3$ by the first term of the divisor $x^2$, which gives us $-11x$.

Step 4 ：Step 4: Multiply the divisor $x^2-3x+1$ by $-11x$ and subtract the result from the new dividend. The result is $-8x^2+28x-11$.

Step 5 ：Step 5: Repeat the process once more, dividing the first term of the new dividend $-8x^2$ by the first term of the divisor $x^2$, which gives us $-8$.

Step 6 ：Step 6: Multiply the divisor $x^2-3x+1$ by $-8$ and subtract the result from the new dividend. The result is $16x-7$, which is the remainder of the division.