1. **State the problem:** We need to find the sum of the polynomials $$6x + 7 + x^2$$ and $$2x^2 - 3$$. 2. **Write the expression for the sum:** $$ (6x + 7 + x^2) + (2x^2 - 3) $$ 3. **Combine like terms:** - Combine the $$x^2$$ terms: $$x^2 + 2x^2 = 3x^2$$ - Combine the $$x$$ terms: $$6x$$ (no like term in second polynomial) - Combine the constants: $$7 - 3 = 4$$ 4. **Write the simplified polynomial:** $$3x^2 + 6x + 4$$ 5. **Answer:** The sum of the polynomials is $$3x^2 + 6x + 4$$. This matches the option: 3 x^2 + 6x + 4.