Final answer:
The polynomial function f(x) = 4 - 2x² - 5x´ has a higher degree than g(x) = 5x³ + 12x² + 2, with the former being fourth degree and the latter being third degree.
Step-by-step explanation:
We need to identify which polynomial function is of a greater degree between f(x) = 4 - 2x² - 5x´ and g(x) = 5x³ + 12x² + 2. The degree of a polynomial is the highest power of the variable x that appears in the polynomial. For the function f(x), the highest power of x is 4, therefore the degree is 4. In the function g(x), the highest power of x is 3, indicating that the degree is 3. Therefore, f(x) is the polynomial of greater degree.