Roots of a Polynomial

A root or zero of a function is a number that, when plugged in for the variable, makes the function equal to zero. Thus, the roots of a polynomial P(x) are values of x such that P(x) = 0.

The Rational Zeros (Roots) Theorem

We can use the Rational Zeros Theorem to find all the rational zeros of a polynomial.

1. 
   Arrange the polynomial in descending order


2. Write down all the factors of the constant term. These are all the possible values of p.


3. Write down all the factors of the leading coefficient (The coefficient of the first term of a polynomialwhen writing in descending order.)
   These are all the possible values of q.


4. Write down all the possible values of p/q . Remember that since factors can be negative p/q, and - (p/q)must both be included. Simplify each value and cross out any duplicates.


5. Use synthetic division or remainder theorem to determine the values of p/q for which P(p/q) = 0. These are all the rational roots of P(x).
   

Example:

Find all the possible rational roots of