# 12.5: Division of Polynomials

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**Practice**Division of Polynomials

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Denominator

The denominator of a fraction (rational number) is the number on the bottom and indicates the total number of equal parts in the whole or the group. has denominator .Dividend

In a division problem, the dividend is the number or expression that is being divided.divisor

In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression , 6 is the divisor and 152 is the dividend.Polynomial long division

Polynomial long division is the standard method of long division, applied to the division of polynomials.Rational Expression

A rational expression is a fraction with polynomials in the numerator and the denominator.Rational Root Theorem

The rational root theorem states that for a polynomial, , where are integers, the rational roots can be determined from the factors of and . More specifically, if is a factor of and is a factor of , then all the rational factors will have the form .Remainder Theorem

The remainder theorem states that if , then is the remainder when dividing by .Synthetic Division

Synthetic division is a shorthand version of polynomial long division where only the coefficients of the polynomial are used.### Image Attributions

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Find the quotient and remainder of rational expressions that involve division.

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Date Created:

Oct 01, 2012
Last Modified:

Apr 11, 2016
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