$\begin{array}{r}3 x^{2}+x+1 \\ -\quad 2 x^{2}+4 x-3 \\ \hline\end{array}$

Step 1 ：Subtract the second polynomial from the first: \( (3x^2 + x + 1) - (2x^2 - 4x + 3) \)

Step 2 ：Combine like terms: \(\boxed{1x^2 - 3x + 4}\)