Maharashtra State BoardSSC (English Medium) 8th Standard
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Division of Algebraic Expressions - Dividing a Monomial by a Monomial

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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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