1. The problem asks to find the product of two functions $f(x) = 2x + 1$ and $g(x) = x^2 - 3x$. 2. The formula for the product of two functions is: $$ (f \times g)(x) = f(x) \cdot g(x) $$ 3. Substitute the given functions into the formula: $$ (f \times g)(x) = (2x + 1)(x^2 - 3x) $$ 4. Use the distributive property (FOIL) to expand the product: $$ (2x + 1)(x^2 - 3x) = 2x \cdot x^2 + 2x \cdot (-3x) + 1 \cdot x^2 + 1 \cdot (-3x) $$ 5. Simplify each term: $$ = 2x^3 - 6x^2 + x^2 - 3x $$ 6. Combine like terms: $$ = 2x^3 - 5x^2 - 3x $$ 7. Therefore, the product function is: $$ (f \times g)(x) = 2x^3 - 5x^2 - 3x $$ 8. Comparing with the options, the correct answer is option D.