Final answer:
The degree of the polynomial function P(x) = 2x^7 - 3x^5 - 7^10 + 2x^8 - x + 3 is 8.
Step-by-step explanation:
The degree of a polynomial is the highest power of x in the polynomial. To find the degree of the given polynomial function P(x), we look for the term with the highest power of x. In this case, the term with the highest power is 2x^8. Therefore, the degree of the polynomial function P(x) is 8.