1. **State the problem:** Add the polynomials \( (3x^3 + 3x^2 - 4x + 5) + (x^3 - 2x^2 + x - 4) \). 2. **Write down the polynomials:** \[ 3x^3 + 3x^2 - 4x + 5 + x^3 - 2x^2 + x - 4 \] 3. **Add like terms:** - Combine \(3x^3\) and \(x^3\): \(3x^3 + x^3 = 4x^3\) - Combine \(3x^2\) and \(-2x^2\): \(3x^2 - 2x^2 = x^2\) - Combine \(-4x\) and \(x\): \(-4x + x = -3x\) - Combine constants \(5\) and \(-4\): \(5 - 4 = 1\) 4. **Write the result:** \[ 4x^3 + x^2 - 3x + 1 \] 5. **Explanation:** When adding polynomials, add coefficients of terms with the same power of \(x\). Constants are added separately. **Final answer:** \(4x^3 + x^2 - 3x + 1\)