Division of Polynomial by Monomial

We at ask-math believe that educational material should be free for everyone. Please use the content of this website for in-depth understanding of the concepts. Additionally, we have created and posted videos on our youtube.

We also offer One to One / Group Tutoring sessions / Homework help for Mathematics from Grade 4th to 12th for algebra, geometry, trigonometry, pre-calculus, and calculus for US, UK, Europe, South east Asia and UAE students.

Affiliations with Schools & Educational institutions are also welcome.

Please reach out to us on [email protected] / Whatsapp +919998367796 / Skype id: anitagovilkar.abhijit

We will be happy to post videos as per your requirements also. Do write to us.

Division of polynomial by monomial = divide each term of a polynomial by the monomial and simplify.

For dividing a polynomial in one variable by a monomial in the same variable, we perform the following steps :

Obtain the polynomial(Dividend) and the monomial(divisor).
Arrange the terms of the dividend in the descending order of their exponents.
Separate the each term using heart method.
Divide each term of the polynomial be the given monomial by using the rules of division of a monomial by a monomial.

Some solved examples:

2) 9m5 + 12m4 - 6m2 ÷ 3m2

Solution :
   9m5 + 12m4 - 6m2
= -------------------
Separate each term using heart method

= (9m5/3m2) + (12m4/3m2) - (6m2/3m2)
= 3m3 + 4m2 - 2
3) 24x3y + 20x2y2 - 4xy ÷ 2xy

Solution :
   24x3y + 20x2y2 - 4xy
= --------------------

= (24x3y/2xy) + (20x2y2/2xy) - (4xy/2xy)
= 12x2 + 10xy - 2
4) x + 2x2 + 3x4 - x5 ÷ by 2x

Solution :
First arrange all the terms in decreasing order of exponents
-x5 + 3x4 + 2x2 + x ÷ 2x

   -x5 + 3x4 + 2x2 + x
= --------------------
= (-x5/2x) + (3x4/2x) + (2x2/2x) + (x/2x)

= (-1/2) x4 + (3/2)x3 + x + 1/2
5) 5x2 - 25x ÷ 5x

Solution :
First arrange all the terms in decreasing order of exponents
5x2 - 25x ÷ 5x

    5x( x - 5)
= ------------
= x -5

Division of Algebraic Expressions

Division of Polynomial by Monomial
Division of Polynomial by Binomial

Algebraic Expression Page

Home Page

Russia-Ukraine crisis update - 3rd Mar 2022

The UN General assembly voted at an emergency session to demand an immediate halt to Moscow's attack on Ukraine and withdrawal of Russian troops.