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Ruffini's rule
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Ruffini's rule
In mathematics, Ruffini's rule is a method for computation of the Euclidean division of a polynomial by a binomial of the form x − r. It was described by Paolo Ruffini in 1809. The rule is a special case of synthetic division in which the divisor is a linear monic factor.
The rule establishes a method for dividing the polynomial:
by the binomial:
to obtain the quotient polynomial:
The algorithm is in fact the long division of P(x) by Q(x).
To divide P(x) by Q(x):
The b values are the coefficients of the result (R(x)) polynomial, the degree of which is one less than that of P(x). The final value obtained, s, is the remainder. The polynomial remainder theorem asserts that the remainder is equal to P(r), the value of the polynomial at r.
Here is an example of polynomial division as described above.
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Ruffini's rule
In mathematics, Ruffini's rule is a method for computation of the Euclidean division of a polynomial by a binomial of the form x − r. It was described by Paolo Ruffini in 1809. The rule is a special case of synthetic division in which the divisor is a linear monic factor.
The rule establishes a method for dividing the polynomial:
by the binomial:
to obtain the quotient polynomial:
The algorithm is in fact the long division of P(x) by Q(x).
To divide P(x) by Q(x):
The b values are the coefficients of the result (R(x)) polynomial, the degree of which is one less than that of P(x). The final value obtained, s, is the remainder. The polynomial remainder theorem asserts that the remainder is equal to P(r), the value of the polynomial at r.
Here is an example of polynomial division as described above.