# Question #43ebe

Jan 16, 2015

Well there is 1 i know ie using synthetic division,

The Rational Zeros Theorem states:
If P(x) is a polynomial with integer coefficients and if is a zero of P(x) ( P() = 0 ), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x) .
We can use the Rational Zeros Theorem to find all the rational zeros of a polynomial. Here are the steps:

Arrange the polynomial in descending order
Write down all the factors of the constant term. These are all the possible values of p .
Write down all the factors of the leading coefficient. These are all the possible values of q .
Write down all the possible values of . Remember that since factors can be negative, and - must both be included. Simplify each value and cross out any duplicates.
Use synthetic division to determine the values of for which P() = 0 . These are all the rational roots of P(x) .