division of polynomial by monomial

# Division of Polynomial by Monomial

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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) 9m
5 + 12m 4 - 6m 2 ÷ 3m 2

Solution :
9m
5 + 12m 4 - 6m 2
= -------------------
3m
2
Separate each term using heart method

= (9m
5 /3m 2 ) + (12m 4 /3m 2 ) - (6m 2 /3m 2 )
= 3m
3 + 4m 2 - 2
_________________________________________________________________
3) 24x
3 y + 20x 2 y 2 - 4xy ÷ 2xy

Solution :
24x
3 y + 20x 2 y 2 - 4xy
= --------------------
2xy

= (24x
3 y/2xy) + (20x 2 y 2 /2xy) - (4xy/2xy)
= 12x
2 + 10xy - 2
_________________________________________________________________
4) x + 2x
2 + 3x 4 - x 5 ÷ by 2x

Solution :
First arrange all the terms in decreasing order of exponents
-x
5 + 3x 4 + 2x 2 + x ÷ 2x

-x
5 + 3x 4 + 2x 2 + x
= --------------------
2x
= (-x
5 /2x) + (3x 4 /2x) + (2x 2 /2x) + (x/2x)

= (-1/2) x
4 + (3/2)x 3 + x + 1/2
________________________________________________________________
5) 5x
2 - 25x ÷ 5x

Solution :
First arrange all the terms in decreasing order of exponents
5x
2 - 25x ÷ 5x

5x( x - 5)
= ------------
5x
= x -5

Division of Algebraic Expressions

Division of Polynomial by Monomial
Division of Polynomial by Binomial

Algebraic Expression Page

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