Step 1 :First, we align the polynomials vertically by their like terms: \[\begin{align*} &3x^3 - 2x^2 + 4x - 1\\ &+2x^3 + 3x^2 - 5x + 2\end{align*}\]
Step 2 :Then, we add the like terms together: \[\begin{align*} &(3x^3 + 2x^3) + (-2x^2 + 3x^2) + (4x - 5x) + (-1 + 2)\\ &=(5x^3) + (x^2) + (-x) + (1)\end{align*}\]
Step 3 :Finally, we write the sum as a single polynomial: \( 5x^3 + x^2 - x + 1 \)