I agree with you: and 8.5 < 10. However, I will say more: this is not a polynomial at least according to Wikipedia because a polynomial must have nonnegative integer exponents.
f(x) = ((sqrt)(3x^17)) + 22.5x^10 - 3x^7 + 1/3
If you can't make that out, it's the square root of 3x^17 for the first term. Now can't one factor out x^16 from under the radical and put x^8 in front? If so, that means the leading term is actually 22.5x^10 and the polynomial actually is of degree 10. My source says it is of degree 17.