The Rational Root Theorem gives a finite list of candidate rational roots for a polynomial with integer coefficients, stating that any rational root, written in lowest terms, must have a numerator dividing the polynomial's constant term and a denominator dividing its leading coefficient. It is a standard tool of elementary algebra for testing a polynomial for rational roots before resorting to numerical methods.
Facts
StatementFor a polynomial equation with integer coefficients, any rational root p/q written in lowest terms must have its numerator p dividing the constant term and its denominator q dividing the leading coefficient, which gives a finite list of candidate rational roots to test. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Sources
1. Rational Root Theorem (Wikipedia)
Wikimedia FoundationStatement section, the p/q-in-lowest-terms sentenceQuote, Statement section, the p/q-in-lowest-terms sentence
written in lowest terms (that is, p and q are relatively prime), satisfies: p is an integer factor of the constant term a0, and q is an integer factor of the leading coefficient an.
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