Final answer:
The Rational Root Theorem is a tool used in algebra to identify possible rational roots or solutions of polynomial equations. It provides a method to determine the factors of the constant and leading coefficients that could result in rational roots. By testing these possible roots, we can find the solutions to the polynomial equation.
Step-by-step explanation:
The Rational Root Theorem is a tool used in algebra to identify possible rational roots or solutions of polynomial equations. It states that if a polynomial equation with integer coefficients has a rational root, it must be a fraction in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
To find the rational roots of a polynomial equation, we can use synthetic division or the long division method to test different possible roots until we find one that satisfies the equation. Once a rational root is found, we can use polynomial division to factorize the equation and find the remaining roots.
For example, let's say we have the equation 2x^3 - x^2 - 6x + 3 = 0. By applying the Rational Root Theorem, we can determine that the possible rational roots are ±1, ±3, and ±1/2. We can then test these values using synthetic division or long division until we find the roots of the equation.