Identify the nth-degree polynomial function with real coefficients that satisfies the following conditions: n = 3, -2 and 2 + 5i are zeros, f(1) = 78.

Find the zeros of the following function: f(x) = x³ + x² - 15x + 9

Find the zeros of the given polynomial function. Use Descartes's Rule of Signs and Rational Zero Theorem. You may also use a graphing utility to help you get the first zero.

f(x) = x³ - x² - 14x + 24

List the possible rational zeros of the following function using the Rational Zero Theorem:

f(x) = 3x⁵ - 5x⁴ - 2x³ +9x² - 15x - 16