1. **State the problem:** We need to find the sum of the two polynomials $-2x^2 + 5x + 10$ and $-7x - 3$. 2. **Formula and rules:** To add polynomials, add the coefficients of like terms (terms with the same power of $x$). 3. **Add like terms:** - The $x^2$ term: $-2x^2$ (no corresponding term in second polynomial) - The $x$ terms: $5x + (-7x) = 5x - 7x$ - The constant terms: $10 + (-3) = 10 - 3$ 4. **Simplify each sum:** $$ 5x - 7x = \cancel{5x} - \cancel{7x} = -2x $$ $$ 10 - 3 = \cancel{10} - \cancel{3} = 7 $$ 5. **Write the final sum:** $$ -2x^2 - 2x + 7 $$ This is the sum of the given polynomials.