1. **State the problem:** We are given two functions $f(x) = x^2 + 9$ and $g(x) = x + 3$. We need to determine which operation among addition, subtraction, multiplication, and division of these functions does NOT result in a polynomial expression. 2. **Recall the definition of a polynomial:** A polynomial is an expression consisting of variables and coefficients, involving only addition, subtraction, multiplication, and non-negative integer exponents of variables. Division by a variable expression generally does NOT produce a polynomial. 3. **Analyze each operation:** - a. $f(x) + g(x) = (x^2 + 9) + (x + 3) = x^2 + x + 12$ which is a polynomial. - b. $f(x) - g(x) = (x^2 + 9) - (x + 3) = x^2 - x + 6$ which is a polynomial. - c. $f(x) \cdot g(x) = (x^2 + 9)(x + 3) = x^3 + 3x^2 + 9x + 27$ which is a polynomial. - d. $\frac{f(x)}{g(x)} = \frac{x^2 + 9}{x + 3}$ which is a rational expression, not a polynomial because of division by a variable expression. 4. **Conclusion:** The operation that does NOT result in a polynomial expression is division, option d. **Final answer:** d. $f(x) \div g(x)$ does not result in a polynomial expression.