# Division of Polynomial by Monomial

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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:**

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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

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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

• Division of Polynomial by Monomial

• Division of Polynomial by Binomial

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