How to factorise of Polynomials

Introduction:
                 In mathematics, a polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents. 

There are various methods of factorising a polynomial. They are,

1. Factorisation by dividing the expression by the HCF of the terms of the given expression.
2. Factorisation by grouping the terms of the expression.
3. Factorisation using identities.
You know that any polynomial of the form p(a) can also be written as

If the remainder is zero, then p(a) = g(a) x h(a). That is, the polynomial p(a) is a product of two other polynomials g(a) and h(a). For example, 3a + 6a² = 3a x (1 + 2a).
It may be possible to express a polynomial as the product of two or more polynomials, in more than one form.

Methods of factorising polynomials:

There are various methods of factorising a polynomial. They are,
1. Factorisation by dividing the expression by the HCF of the terms of the given expression.
2. Factorisation by grouping the terms of the expression.
3. Factorisation using identities.