“Polynomial Remainder Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Polynomial Remainder Theorem

释义

Polynomial Remainder Theorem

If the Coefficients of the Polynomial

(1)

are specified to be Integers, then integral Roots must have a Numerator which is afactor of

and a Denominator which is a factor of

(with either sign possible). This follows since aPolynomial of Order

with

integral Roots can be expressed as

(2)

where the Roots are

, ..., and

. Factoring out the

(3)

Now, multiplying through,

(4)

where we have not bothered with the other terms. Since the first and last Coefficients are

and

, all the integral roots of (1) are of the form [factors of

]/[factors of

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