Guidelines for FInding the zeros of a polynomial function with integer coefficients

1. Gather general information. Determine the degree N of the polynomial function. The number of the distinct zeros of the polynomial function is at most N
Apply Descartes' Rule of Signs to find the possible number of positive zeros and also the possible number of negative zeros

2. Check suspects. Apply the Rational Zero Theorem to list rational numbers that are possible zeros. Use syn div to test the numbers in your list. If you find an upper or lower bound then eliminate from your list any number that is greater than the upper bound or less than the lower bound

3 Work with reduced polynomials. each time a s zero is found, you obtain a reduced polynomial

if a reduced polynomial is of degree 2, find its zeros either by factoring or by applying the quadratic formula.

if the degree of a reduced polynomial is 3 or greater repeat the above steps for this polynomial.