# Factorisation

## Factorisation

### Factors of Algebraic Expressions

We have already learnt prime factor form wherein a number is written as product of prime factors. Similarly we can factorise an algebraic expression.

The irreducible factor of an algebraic term is a factorof the term that cannot be further factorised. Analgebraic expression written as the product of itsirreducible factors is called the irreducible form of the term.
Expressing an algebraic expression as the product of its factors is called the factorisation of the expression. This is the factor form of the expression.
The factors of an algebraic expression may be numbers or algebraic expression. The basic methods to factorise an algebraic expression are:
• Identifying the common factors
• Regrouping the terms
• Using algebraic identities
The basic identities used to factorise an algebraic expressions are:

We have learnt addition, subtraction and multiplication of algebraic expressions. In this lesson we will learn how to divide algebraic expressions.

In case of numbers Division is the inverse operation of multiplication but the same is applicable for thedivision of algebraic expressions also. To divide a monomial by a monomial, first express the numeratorand the denominator in their irreducible form, and then cancel the common factors. To divide apolynomial by a monomial, either divide each term of the numerator by the denominator or factorise the numerator by the common factor method. To divide apolynomial by a polynomial, first factorise the numerator and the denominator by using the appropriate method and then cancel the common factors.

### Division of Algebraic Expression

In case of numbers Division is the inverse operation of multiplication but the same is applicable for the division of algebraic expressions also.

Division of a monomial by another monomial
To divide a monomial by a monomial, first express the numerator and the denominator in their irreducible form, and then cancel the common factors.

Division of a polynomial by a monomial
To divide a polynomial by a monomial, either divide each term of the numerator by the denominator or factorise the numerator by the common factor method.

Division of a polynomial by a polynomial
To divide a polynomial by a polynomial, first factorise the numerator and the denominator by using the appropriate method and then cancel the common factors.

Dividend = Divisor × Quotient + Remainder.

Hint: Division is the inverse operation of multiplication.
2x × (2x+3) = 4x2 + 6x, then
(4x2 + 6x) ÷ 2x = (2x+3)