Class 8 Maths Factorisation Division of Algebraic Expressions

Division of Algebraic Expressions

Till now, we have learnt how to add, subtract and multiply the algebraic expressions. Now, we see at

division of one algebraic expression by another.

Division of a Monomial by another Monomial:

Let us take an example.

Ex: Let we want to divide 12x4 by 3x2

Now, we write 12x4 by 3x2 in irreducible factor forms as

12x4 = 2 * 2 * 3 * x * x * x * x

3x2 = 3 * x * x

So, 12x4 / 3x2 = (2 * 2 * 3 * x * x * x * x)/(3 * x * x)

                         = 4 * x * x                   [Cancel of common terms]

                         = 4x2  

Division of a polynomial by a monomial:

Let we want to divide a polynomial 2x3 + 7x2 + 6x by 2x

2x3 + 7x2 + 6x = 2 * x * x * x + 7 * x * x + 2 * 3 * x

2x = 2 * x

Now, (2x3 + 7x2 + 6x)/2x = (2 * x * x * x + 7 * x * x + 2 * 3 * x)/(2 * x)

                                           = [2x * x2 + 2x * (7x/2) + 2x * 3]/2x

                                           = [2x{x2 + 7x/2 + 3}]/2x

                                           = x2 + 7x/2 + 3    

We can also do the division in another way.

(2x3 + 7x2 + 6x)/2x = 2x3 /2x+ 7x2 /2x + 6x/2x

                                 = x2 + 7x/2 + 3 

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