1. The problem asks for the correct form of the partial fraction decomposition of the rational expression with denominator $(x - 8)(x^2 + 8)$. 2. When decomposing a rational function, the denominator is factored into linear and irreducible quadratic factors. 3. For a linear factor like $(x - 8)$, the numerator in the partial fraction is a constant $A$. 4. For an irreducible quadratic factor like $(x^2 + 8)$, the numerator is a linear polynomial $Bx + C$. 5. Therefore, the partial fraction decomposition form is: $$\frac{A}{x - 8} + \frac{Bx + C}{x^2 + 8}$$ 6. Comparing this with the options, option D matches this form exactly. 7. Hence, the correct answer is option D: $\frac{A}{x - 8} + \frac{Bx + C}{x^2 + 8}$.