1. The problem asks to find the function $(f+g)(x)$, which means we need to add the functions $f(x)$ and $g(x)$ together. 2. Given: $$f(x) = 3x^2 + 5x$$ $$g(x) = x^2 + 6x + 5$$ 3. The formula for adding two functions is: $$(f+g)(x) = f(x) + g(x)$$ 4. Substitute the given functions: $$(f+g)(x) = (3x^2 + 5x) + (x^2 + 6x + 5)$$ 5. Combine like terms: $$3x^2 + x^2 + 5x + 6x + 5 = (3x^2 + x^2) + (5x + 6x) + 5$$ $$= 4x^2 + 11x + 5$$ 6. The polynomial is already in simplest form. Final answer: $$(f+g)(x) = 4x^2 + 11x + 5$$