<\/p>\n
When an expression is the product of two or more expressions, then each of the expressions is called a factor of the given expression.<\/p>\n
The process of writing a given expression as the product of two or more factors is called factorization.<\/p>\n
The greatest common factor of two or more monomials is the product of the greatest common factors of the numerical coefficients and the common letters with smallest powers.<\/p>\n
When a common monomial factor occurs in each term of an algebraic expression, then it can be expressed as a product of the greatest common factor of its terms and quotient of the given expression by the greatest common factor of its terms.<\/p>\n
When a binomial is a common factor, we write the given expression as the product of this binomial and the quotient of the given expression by this binomial.<\/p>\n
If the given expression is the difference of two squares, then to factorize it, we use the formula (a2<\/sup> \u2013 b2<\/sup>) = (a + b) (a \u2013 b)<\/p>\n If the given expression is a complete square, we use one of the following formulae to factorize it:<\/p>\n For factorisation of the form (x2<\/sup> + px + q), we find two numbers a and b such that (a + b) = p and ab = q, then x2<\/sup> + px + q = x2<\/sup> + (a + b)x + ab = (x + a) (x + b).<\/p>\n In case of division of a polynomial by a monomial, we may carry out the division either by dividing each term of the polynomial by the monomial or by the common factor method.<\/p>\n In case of division of a polynomial by a polynomial, we cannot proceed by dividing each term in the dividend polynomial by the division polynomial. Instead, we factorise both the polynomial and cancel their common factors.<\/p>\n In the case of division of algebraic expression, we have Dividend = Divisor \u00d7 Quotient + Remainder.<\/p>\n Factors of Natural Numbers<\/strong> Factors of Algebraic Expressions<\/strong> What is Factorisation?<\/strong> Method of Common Factors<\/strong> Factorisation By Regrouping Terms<\/strong> Factorisation Using Identities<\/strong> Factors of the Form (x + a) (x + b)<\/strong> Division of Algebraic Expressions Division of a Monomial by Another Monomial<\/strong> Division of a Polynomial by a Monomial<\/strong> Division of Algebraic Expressions Continued (Polynomial \u00f7 Polynomial)<\/strong> Rules to be Followed You Find The Errors<\/strong><\/p>\n We hope the given CBSE Class 8 Maths Notes Chapter 14 Factorisation Pdf free download will help you. If you have any query regarding NCERT Class 8 Maths Notes Chapter 14 Factorisation, drop a comment below and we will get back to you at the earliest.<\/p>\n","protected":false},"excerpt":{"rendered":" CBSE Class 8 Maths Notes Chapter 14 Factorisation When an expression is the product of two or more expressions, […]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Get CBSE Class 8 Maths Notes Chapter 14 Factorisation to infinity learn.","custom_permalink":"study-material\/factorisation\/class-8\/notes\/maths\/chapter-14\/"},"categories":[92,21],"tags":[],"table_tags":[],"acf":[],"yoast_head":"\n\n
\nA number, when written as a product of its prime factors, is said to be in the prime factor form. Similarly, we can express algebraic expressions as products of their factors.<\/p>\n
\nAn irreducible factor is one which cannot be expressed further as a product of factors.<\/p>\n
\nWhen we factorise an algebraic expression, we write it as a product of irreducible factors. These factors may be numbers, algebraic variables or algebraic expressions.<\/p>\n
\nWe factorise each term of the given algebraic expression as a product of irreducible factors and separate the common factors. Then, we combine the remaining factors in each term using the distributive law.<\/p>\n
\nSometimes it so happens that all the terms in a given algebraic expression do not have a common factor; but the terms can be grouped in such a manner that all the terms in each group have a common factor. In doing so, we get a common factor across all the groups formed. This leads to the required factorisation of the given algebraic expression.<\/p>\n
\nThe following identities prove to be quite helpful in factorisation of an algebraic expression:
\n(a + b)2<\/sup> = a2<\/sup> + 2ab + b2<\/sup>
\n(a \u2013 b)2<\/sup> = a2<\/sup> \u2013 2ab + b2<\/sup>
\n(a + b) (a \u2013 b) = a2<\/sup> \u2013 b2<\/sup><\/p>\n
\n(x + a) (x + b) = x2<\/sup> + (a + b) x + ab
\nTo factorise an algebraic expression of the type x2<\/sup> + px + q, we find two factors a and b of q such that ab = q and a + b = p
\nThen, the given expression becomes
\nx2<\/sup> + (a + b) x + ab = x2<\/sup> + ax + bx + ab = x (x + a) + b (x + b) = (x + a) (x + b) which are the required factors.<\/p>\n
\nHere, we shall divide one algebraic expression by another.<\/p>\n
\nWe shall factorise the numerator and denominator into irreducible factors and cancel out the common factors from the numerator and the denominator.<\/p>\n
\nWe divide each term of the polynomial in the numerator by the monomial in the denominator.<\/p>\n
\nWe factorise the algebraic expressions in the numerator and the denominator into irreducible factors and cancel the common factors from the numerator and the denominator.<\/p>\n\n