Final answer:
To find the zeros of the cubic polynomial p(x) = x³ - 7x² + 7x + 15, one might need to resort to factoring, using the Rational Root Theorem, or applying numerical methods if factoring is not feasible.
Step-by-step explanation:
To find the zero of the polynomial p(x) = x³ - 7x² + 7x + 15, one method is to attempt to factor the polynomial, or another approach is to use numerical methods or algorithms that approximates the roots. Factoring can sometimes be straightforward, but for higher degree polynomials, it often requires the trial and error of potential rational roots or the use of the Rational Root Theorem. However, if the polynomial cannot be easily factored, numerical methods such as Newton's method can be employed to find an approximation of the zeros.
Given the complexity of the polynomial, a systematic approach or a calculator with capabilities to solve cubic equations may be necessary to accurately determine the zeroes of p(x).