1. The problem asks to find $(g - h)(x)$ where $g(x) = 5x^3 + 16x + 7$ and $h(x) = 2x^3 - 5x + 8$. 2. The formula for subtraction of functions is $(g - h)(x) = g(x) - h(x)$. 3. Substitute the given functions: $$ (g - h)(x) = (5x^3 + 16x + 7) - (2x^3 - 5x + 8) $$ 4. Distribute the minus sign: $$ (g - h)(x) = 5x^3 + 16x + 7 - 2x^3 + 5x - 8 $$ 5. Combine like terms: $$ (g - h)(x) = (5x^3 - 2x^3) + (16x + 5x) + (7 - 8) $$ $$ (g - h)(x) = 3x^3 + 21x - 1 $$ 6. The degree of the polynomial is the highest power of $x$, which is 3, so it is a cubic polynomial. Final answer: $(g - h)(x) = 3x^3 + 21x - 1$; cubic polynomial.