Final answer:
To find the potential rational solutions of a polynomial equation, use the Rational Root Theorem. The potential rational solutions are ±1, ±3, ±11, and ±33.
Step-by-step explanation:
Polynomial Equation and Rational Solutions:
To find the potential rational solutions of the polynomial equation x³ - 9x² - 25x + 33 = 0, we can use the Rational Root Theorem. According to this theorem, any rational root of the equation can be expressed as p/q, where p is a factor of the constant term (33) and q is a factor of the leading coefficient (1).
In this case, the factors of 33 are ±1, ±3, ±11, ±33, and the factors of 1 are ±1. Therefore, the potential rational solutions are:
- x = ±1
- x = ±3
- x = ±11
- x = ±33