1. **State the problem:** We are given two functions $f(x) = x^2 + 13x + 40$ and $g(x) = x + 8$. We need to find the sum $f(x) + g(x)$ and express it as a simplified polynomial. 2. **Write the sum:** $$f(x) + g(x) = (x^2 + 13x + 40) + (x + 8)$$ 3. **Combine like terms:** Group the $x^2$ terms, the $x$ terms, and the constant terms: $$x^2 + (13x + x) + (40 + 8)$$ 4. **Simplify the sums inside parentheses:** $$x^2 + 14x + 48$$ 5. **Final answer:** The sum of the two functions expressed as a polynomial in simplest form is: $$f(x) + g(x) = x^2 + 14x + 48$$