4. Manu determines the roots of a polynomial equation by applying the theorems he knows. He organizes the results of these theorems.
From the fundamental theorem of algebra, Manu knows there are 3 roots to the equation.
From Descartes’ rule of sign, Manu finds no sign changes in and 3 sign changes in .
The rational root theorem yields as the list of possible rational roots.
The lower bound of the polynomial is .
The upper bound of the polynomial is 1.
What values in Manu’s list of rational roots should he try in synthetic division in light of these findings?