Rational Zero Theorem

Definition

The Rational Zero Theorem states that any rational root of a polynomial equation with integer coefficients is a fraction $\frac{p}{q}$, where $p$ is a factor of the constant term and $q$ is a factor of the leading coefficient.

5 Must Know Facts For Your Next Test

1. To apply the Rational Zero Theorem, list all factors of the constant term and the leading coefficient.
2. Rational zeros are potential candidates and must be tested in the polynomial to confirm if they are actual roots.
3. The theorem helps in narrowing down possible rational roots but does not guarantee their existence.
4. The Rational Zero Theorem only applies to polynomials with integer coefficients.
5. If a polynomial has no rational roots, then none of the fractions formed by $\frac{p}{q}$ will satisfy the polynomial.

Review Questions

Related terms

Polynomial Function:

A function that is defined by a polynomial, or an expression involving sums and products of variables and coefficients.

Factorization:

The process of breaking down a polynomial into its component factors.

Synthetic Division:

$A simplified method for dividing polynomials as an alternative to long division.$