1. **State the problem:** We need to find the sum of the two polynomials $x^2 + 3x - 9$ and $4x^2 - 6x + 1$. 2. **Formula and rules:** When adding polynomials, combine like terms. Like terms have the same variable raised to the same power. 3. **Add the polynomials:** $$ (x^2 + 3x - 9) + (4x^2 - 6x + 1) = x^2 + 3x - 9 + 4x^2 - 6x + 1 $$ 4. **Group like terms:** $$ (x^2 + 4x^2) + (3x - 6x) + (-9 + 1) $$ 5. **Simplify each group:** $$ 5x^2 - 3x - 8 $$ 6. **Final answer:** The sum of the polynomials is $5x^2 - 3x - 8$. Therefore, the correct choice is **B) 5x^2 - 3x - 8**.