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7.12: Division of a Polynomial by a Monomial

Difficulty Level: Advanced Created by: CK-12
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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. \frac{5}{8} has denominator 8.


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


In a division problem, the divisor is the number or expression that is being divided into the dividend. For example: In the expression 152 \div 6, 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, f(x)=a_nx^n+a_{n-1}x^{n-1}+\cdots+a_1x+a_0, where a_n, a_{n-1}, \cdots a_0 are integers, the rational roots can be determined from the factors of a_n and a_0. More specifically, if p is a factor of a_0 and q is a factor of a_n, then all the rational factors will have the form \pm \frac{p}{q}.

Remainder Theorem

The remainder theorem states that if f(k) = r, then r is the remainder when dividing f(x) by (x - k).

Synthetic Division

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

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