Division of Polynomial by a Monomial


 
 
Concept Explanation
 

Division of a Polynomial by a Monomial

A monomial can have only one term and a polynomial can have any number of terms. Division of a polynomial with a monomial involves dividing each term of the polynomial with the monomial. For dividing a polynomial in one variable by a monomial in the same variable, we perform the following steps :

Step I     Obtain the polynomial  (dividend) and the monomial (divisor).

Step II    Arrange the terms of the dividend in descending order of their degrees.

              For example, write 6x^{2};+;7x;-;3;+;5x^{3};;as;;5x^{3};+;6x^{2};+;7x;-;3

Step III   Divide each term of the polynomial by the given monomial by using the rules of division of a

              monomial  by a monomial.

Illustration: Divide 9m^5+12m^4-6m^2  by  3m^2    

Solution:  To divide the monomial we will perform the following steps: 

frac{9m^{5}+12m^{4}-6m^{2}}{3m^{2}}

=frac{9m^{5}}{3m^{2}};;+;;frac{12m^{4}}{3m^{2}};;-;;frac{6m^{2}}{3m^{2}};

 =;3m^{2};;+;;4m^{2};;-;;2

Illustration: Divide 24x^{3}y;+;20x^{2}y^{2};-;4xy  by  2xy

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Sample Questions
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Question : 1

What is the quotient when polynomial 44x^2+99x is divided by 11x ?

Right Option : C
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Question : 2

Simplify: frac{-9g+12}{-3}

Right Option : A
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Question : 3

What is the quotient when polynomial 22x^2+33x is divided by 11x ?

Right Option : A
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Explanation
 
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