Scribd
Upload
72 views3 pages

Factorisation CHCKKH

Division of algebraic expressions can be done in several ways: 1) Division of a monomial by another monomial, such as 9x divided by 3 equals 3x. 2) Division of a polynomial by a monomial using long division, such as dividing 2x^3 + 4x^2 + 6x by 2x. 3) Division of a polynomial by another polynomial using long division, such as dividing 3x^2 + 3x - 5 by (x - 1).

Uploaded by

Raj Kumar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
72 views3 pages

Factorisation CHCKKH

Division of algebraic expressions can be done in several ways: 1) Division of a monomial by another monomial, such as 9x divided by 3 equals 3x. 2) Division of a polynomial by a monomial using long division, such as dividing 2x^3 + 4x^2 + 6x by 2x. 3) Division of a polynomial by another polynomial using long division, such as dividing 3x^2 + 3x - 5 by (x - 1).

Uploaded by

Raj Kumar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
You are on page 1/ 3

Division of Algebraic Expressions

Division of a monomial by another monomial

Division of a monomial by another monomial:


i) Division of 9x by 3: 2

2
3(3x )
2 2
9x ÷3 = = 3x
3

ii) Division of 6x 2
y by 2y:
2 2
6x y 2y(3x )
2 2
6x y ÷ 2y = = = 3x
2y 2y

Division of a polynomial by a monomial

A polynomial 2x 3
+ 4x
2
+ 6x is divided by monomial 2x as shown below:
3 2
(2x +4x +6x) 3 2
2x 4x 6x
2
= + + = x + 2x + 3
2x 2x 2x 2x

Division of a polynomial by a polynomial

Long division method is used to divide a polynomial by a polynomial.


Example:Division of 3x + 3x − 5 by (x − 1) is shown below:
2

Introduction to Factorisation
Factors of natural numbers
Every number can be expressed in the form of product of prime factors. This is called prime
factor form.
Example: Prime factor form of 42 is 2 × 3 × 7, where 2, 3 and 7 are factors of 42.

Algebraic expressions

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables
(like x or y) and operators (like add,subtract,multiply and divide). For example: x + 1, p - q, 3x,
2x+3y, 5a/6b etc.

Factors of algebraic expressions and factorisation

An irreducible factor is a factor which cannot be expressed further as a product of factors.


Algebraic expressions can be expressed in irreducible form.

Example: 7 × (x + 3) is written as 7 × x × (x + 3), where 7, x and (x + 3) are the irreducible


factors of expression 7x(x + 3).

Method of Common Factors


Factorisation by common factors

To factorise an algebraic expression, the highest common factors are determined.


Example: Algebraic expression −2y + 8y can be written as 2y(−y + 4), where 2y is the highest
2

common factor in the expression.

Factorisation by regrouping terms

In some algebraic expressions, it is not possible that every term has a common factor.
Therefore, to factorise those algebraic  expressions, terms having common factors are grouped
together.

Example:
12a + n − na − 12

= 12a − 12 + n − na

= 12(a − 1) − n(a − 1)

= (12 − n)(a − 1)

(12 − n) and (a − 1) are factors of the expression 12a + n − na − 12


 
 

Method of Identities
Algebraic identities

The algebraic equations which are true for all values of variables in them are called algebraic
identities.
Some of the identities are,
2 2 2
(a + b) = a + 2ab + b

2 2 2
(a − b) = a − 2ab + b

2 2
(a + b)(a − b) = a −b

Factorisation using algebraic identities

Algebraic identities can be used for factorisation


Example:
(i) 9x2
+ 12xy + 4y
2

2 2
= (3x) + 2 × 3x × 2y + (2y)

2
= (3x + 4y)

(ii) 4a 2
−b
2
= (2a − b)(2a + b)

Visualisation of factorisation

The algebraic expression x 2


+ 8x + 16 can be written as (x + 4) . This can be visualised as
2

shown below:

You might also like