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**NCERT / CBSE NOTES : Chapter Summary**

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__Factorisation__

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**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**factor**of the**term**that cannot be further**factorised**. An**algebraic expression**written as the**product of its****irreducible 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 the**division of algebraic expressions**also. To**divide a monomial by a monomial**, first express the**numerator**and the**denominator**in their**irreducible****form**, and then cancel the**common****factors**. 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**. 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**.###
** 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) = 4x

^{2}+ 6x, then
(4x

^{2}+ 6x) ÷ 2x = (2x+3)
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