Solution:
1. Write down the given polynomials:
- First polynomial: g(x) = x^3 - 2x^2 + 3x - 1
- Second polynomial: 4x^2 - x + 2
2. Align and add the polynomials term by term:
- g(x) = x^3 - 2x^2 + 3x - 1
- 4x^2 - x + 2
3. Add the corresponding like terms:
- For x^3 terms: x^3
- For x^2 terms: -2x^2 + 4x^2 = 2x^2
- For x terms: 3x - x = 2x
- For constant terms: -1 + 2 = 1
4. The resulting polynomial after addition is:
x^3 + 2x^2 + 2x + 1