# Summary

• Each expression can be written as the product of factors. These factors may be numbers, algebraic variables or algebraic expressions.
• An irreducible factor is a factor which cannot be expressed further as a product of factors.
• The process of writing an algebraic expression as the product of two or more algebraic expressions is called factorisation.
• The following steps are used in the method of common factors.
• Each term of the expression is written as a product of irreducible factors.
• Separate the common factors and
• By distributive law we can combine the remaining factors.
• The terms in an expression are grouped in such a way that we can find a common factor in each group. When we do in this manner, we can find a common factor between the groups which leads to the factorization of the given expression. This method of finding the factors for the given expression is called regrouping.
• Some of the expressions are of the form and These expressions can be easily factorised using identities.
• In the expression of type , we find that the numerical term is the product of the terms ab and and the coefficient of x is the sum of the terms a + b.
• In division of a polynomial by a monomial we may carryout the division either by the common factor method or dividing each term of the polynomial by the monomial (cancellation method).
• In the case of division of polynomial by a polynomial we factorise both the polynomials and cancel their common factors.