1. **State the problem:** Find the sum of the polynomials \( (2x^2 + 5) + (-x^2 + 4) \). 2. **Write the polynomials:** \[ 2x^2 + 5 \] \[ -x^2 + 4 \] 3. **Add like terms:** - Combine the \( x^2 \) terms: \( 2x^2 + (-x^2) = (2 - 1)x^2 = x^2 \) - Combine the constant terms: \( 5 + 4 = 9 \) 4. **Write the sum:** \[ x^2 + 9 \] 5. **Explain:** When adding polynomials, you add coefficients of like terms (terms with the same variable and exponent). Constants are combined separately. **Final answer:** \( x^2 + 9 \)