What does the Rational Zero theorem state for

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 orderWrite 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).

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