Use the rational roots theorem. If a polynomial equation with rational coefficients has a rational root, then that root will be of the form where is an even divisor of the constant term of the equation and is an even divisior of the lead coefficient. Possible rational roots are , , , and .
Use synthetic division to find the first real and rational root. This is an equation of odd degree with rational coefficients, hence there must be at least one real root and it must be rational. Review the process of synthetic division at Purple Math: Synthetic Division Be certain to review all four pages.
The quotient from your successful synthetic division will provide the coeffients of a quadratic equation. From these coefficients, you can calculate the discriminant to determine the character of the remaining two roots.
John
My calculator said it, I believe it, that settles it
