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Polynomial Division Check in Function Notation
A polynomial division problem can be checked by verifying that the dividend equals the product of the quotient and the divisor, plus the remainder. When dividing a polynomial function by a binomial divisor of the form , this relationship can be written in function notation as , where is the quotient and is the remainder. Evaluating this function at involves substituting for , resulting in the equation . Because the term simplifies to , the equation becomes , which reduces to . This mathematical proof demonstrates that evaluating the original polynomial function at yields the exact value of the remainder.
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Intermediate Algebra @ OpenStax
Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax
Algebra
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Polynomial Division Check in Function Notation
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