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For the sake of simplicity, in the sequel a (Laurent) polynomial of negative degree is understood to be the zero polynomial and, similarly, a banded matrix with negative bandwidth reduces to the zero matrix.
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:f 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: