# Division of Algebraic Expressions - Dividing a Monomial by a Monomial

## Notes

### Division of a monomial by another monomial:

In the case of division of a polynomial by a monomial, we may carry out the division either by dividing each term of the polynomial by the monomial or by the common factor method.

Consider 6x3 ÷ 2x
We may write 2x and 6x3 in irreducible factor forms,
2x = 2 xx x
6x^3 = 2 xx 3 xx x xx x xx x
Now we group factors of 6x3 to separate 2x,
6x^3 = 2 xx x xx (3 xx x xx x) = (2x) xx (3x^2)
Therefore, 6x3 ÷ 2x = 3x2
Similarly,
6x^3 ÷ 2x = (6x^3)/(2x)
= (2 xx 3 xx x xx x xx x)/(2 xx x)
= 3 xx x xx x
= 3x^2

## Example

Do the following division.

-20x4 ÷ 10x2

-20x^4 = -2 xx 2 xx 5 xx x xx x xx x xx x

10x^2 = 2 xx 5 xx x xx x

Therefore,
(- 20x^4) ÷ 10x^2

= (-2 xx 2 xx 5 xx x xx x xx x xx x)/(2 xx 5 xx x xx x)

= -2 xx x xx x

= -2x^2

## Example

Do the following division.

7x2y2z2 ÷ 14xyz

7x2y2z2 ÷ 14xyz

=  (7 xx x xx x xx y xx y xx z xx z)/(2 xx 7 xx x xx y xx z)

= (x xx y xx z)/2

= 1/2 xyz

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