Revision Notes: Factorisation | Mathematics Class 9 ICSE PDF Download

Important Concepts 

• When a polynomial is the product of two or more polynomials, each of the later polynomials is called its factors. 
• The method of expressing a given polynomial as a product of two or more polynomials is called factorization. 
• If a given polynomial contains a common factor which may be either a constant or a variable, we divide each term separately by this factor. 
  Example: Each term of the expression 3a² - 9ab has 3a as a common factor. 
  Therefore, we have 3a² - 9ab = 3a(a - ab)
• If the polynomial has even number of terms, then the terms are first arranged in groups such that each group has a common factor.
  Example: Factorise : a³ + a -3a² - 3
  
  
  
• If the polynomial is trinomial in nature, i.e. , it has 3 terms ,we first arrange the terms in descending order. 
  Then, split the middle term in such a way that the product is equal to the product of first and the last term. 
  Example:  Factorise a² + 10a + 24
  
  
  
• Factorisation using difference of two squares: x² - y² = (x + y)(x - y)
  Example: Factorise 9a² + 3a - 8b - 64b²
   
  
  = (3a - 8b)(3a + 8b + 1) [Taking (3a - 8b) common]
• Sum of Difference of Two Cubes: