Rational root theorem facts for kids

The Rational root theorem (or rational zero theorem) is a proven idea in mathematics. It says that if the coefficients of a polynomial are integers, then one can find all of the possible rational roots by dividing each factor of the constant term by each factor of the leading coefficient. ^[1][2]

Think about this polynomial: a_nxⁿ + a_n-1x^n-1 + a_n-2x^n-2 + … + a₀

All of the possible rational roots are these: ±factors of a₀ / ±factors of a_n

This only finds the rational roots. There may be imaginary roots. Other theorems, such as Descartes’ rule of signs, help find how many imaginary roots there are for a given equation. ^[1]

Example

Think about this polynomial: 15x⁴ + 2x³ – 10x² + x – 8

Factors of the leading coefficient are: 15: ±1,±3,±5,±15

Factors of the constant are: -8: ±1,±2,±4,±8

Possible rational roots are: ±1/1,±2/1,±4/1,±8/1,±1/3,±2/3,±4/3,±8/3,±1/5,±2/5,±4/5,±8/5,±1/15,±2/12,±4/15,±8/15

1. Larson, Ron. Algebra 2. Evanston, IL: McDougal Littell, 2007. Print.
2. Phillip S. Jones, Jack D. Bedient: The historical roots of elementary mathematics. Dover Courier Publications 1998, ISBN: 0-486-25563-8, pp. 116–117

See also

In Spanish: Teorema de la raíz racional para niños