Ruffini's rule has many practical applications; most of them rely on simple division (as demonstrated below) or the common extensions given still further below.A worked example of polynomial division, as described above. It can be shown that this remains true for non-monic polynomials, i.e.
If the resulting quotient has no remainder, we have found a root.
You can choose one of the following three methods: they will all yield the same results, with the exception that only through the second method and the third method (when applying Ruffini's rule to obtain a factorization) can you discover that a given root is repeated.
(Neither method will discover irrational or complex roots.) We try to divide P(x) by the binomial (x − each possible root).
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chart is examined to determine if the sample mean is also in statistical control.
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The algorithm is in fact the long division of P(x) by Q(x). Take the coefficients of P(x) and write them down in order.
Then write r at the bottom left edge, just over the line: The b values are the coefficients of the result (R(x)) polynomial, the degree of which is one less than that of P(x). As shown in the polynomial remainder theorem, this remainder is equal to P(r), the value of the polynomial at r.