Mathematics · Polynomial Functions · Topic 8 · 8 of 18
Rational Root Theorem and Factoring
List possible rational roots and factor higher-degree polynomials.
Possible rational roots± factors of the constant term divided by factors of the leading coefficient.
Test candidatesUse substitution or synthetic division.
Factor completelyContinue until each remaining factor is linear or irreducible at this level.
Example
2x³−3x²−8x+12
Possible roots include ±1, ±2, ±3, ±4, ±6, ±12 and their halves. Testing reveals factors that reduce the polynomial.