Final answer:
To find the upper limit of the zeros for the polynomial function P(x) = 4x^4 + 8x^3 - 7x^2 - 21x - 9, one could potentially use Descartes' Rule of Signs or the Rational Root Theorem, disciplines within high school Mathematics.
Step-by-step explanation:
The subject of the question is related to finding the zeros of a polynomial function within the field of mathematics, specifically at the high school level. The function in question is P(x) = 4x^4 + 8x^3 - 7x^2 - 21x - 9. To find the upper limit of the zeros of this function, we can use the Descartes' Rule of Signs or the Rational Root Theorem. Unfortunately, without additional instructions, this question cannot be answered with precision as it requires a method to estimate or find the zeros of the polynomial.