To simplify the polynomial \((x^2 - 4x + 3) + (2x^2 + 2x - 1)\), we will combine like terms.
1. Identify the like terms:
- \(x^2\) terms: \(x^2 + 2x^2\)
- \(x\) terms: \(-4x + 2x\)
- Constant terms: \(3 - 1\)
2. Combine the like terms:
- \(x^2\) terms: \(x^2 + 2x^2 = 3x^2\)
- \(x\) terms: \(-4x + 2x = -2x\)
- Constant terms: \(3 - 1 = 2\)
3. Write the simplified polynomial in standard form:
\[
3x^2 - 2x + 2
\]
Thus, the simplified polynomial is \(3x^2 - 2x + 2\).