Ruffini's rule for polynomial division

E1030529

mathematical algorithm method of polynomial division synthetic division technique

Ruffini's rule for polynomial division is a simplified algorithm for dividing polynomials by linear factors, often used as a shortcut form of synthetic division.

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Observed surface forms (1)

Surface form	Occurrences
Ruffini's rule for synthetic division	1

Statements (47)

Predicate	Object
instanceOf	mathematical algorithm ⓘ method of polynomial division ⓘ synthetic division technique ⓘ
advantage	reduces computational effort compared to long division ⓘ reduces risk of algebraic transcription errors ⓘ
appliesTo	division by binomials of the form x − a ⓘ univariate polynomials ⓘ
assumes	missing powers have coefficient zero ⓘ polynomial coefficients are ordered by descending powers of x ⓘ
basedOn	Horner's method NERFINISHED ⓘ synthetic division ⓘ
category	algorithm in elementary algebra ⓘ
computes	value of the polynomial at x = a as the final remainder ⓘ
countryOfOrigin	Italy ⓘ
developedBy	Paolo Ruffini NERFINISHED ⓘ
field	algebra ⓘ polynomial algebra ⓘ
historicalPeriod	early 19th century ⓘ
input	coefficients of the dividend polynomial ⓘ root a such that divisor is x − a ⓘ
limitation	does not directly handle non-linear divisors ⓘ requires rewriting non-monic linear divisors into monic form ⓘ
namedAfter	Paolo Ruffini NERFINISHED ⓘ
notation	tabular arrangement of coefficients and root value ⓘ
output	coefficients of the quotient polynomial ⓘ remainder of the division ⓘ
property	algorithmic and stepwise ⓘ avoids writing variable symbols during computation ⓘ more compact than long polynomial division ⓘ suitable for hand computation ⓘ uses only addition and multiplication operations ⓘ
relatedTo	Horner's scheme NERFINISHED ⓘ factor theorem ⓘ long division of polynomials ⓘ remainder theorem ⓘ root-finding for polynomials ⓘ
requires	coefficients of the dividend polynomial ⓘ divisor to be a monic linear polynomial in x ⓘ
taughtIn	high school algebra courses ⓘ introductory university algebra courses ⓘ
usedFor	applying the factor theorem ⓘ applying the remainder theorem ⓘ computing polynomial quotients ⓘ computing polynomial remainders ⓘ dividing polynomials by linear factors ⓘ evaluating polynomials at a given value ⓘ testing candidate roots of polynomials ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Paolo Ruffini → knownFor → Ruffini's rule for polynomial division ⓘ

Paolo Ruffini → notableWork → Ruffini's rule for polynomial division ⓘ

this entity surface form: Ruffini's rule for synthetic division