Solving Quadratic Equations by Factorisation
The process of writing an expression as a product of two or more common factors is called the method of factorization. For example:
In the above examples, are the factors of expression , are the factors of and are the factors of .
While solving the quadratic equation by the method of factorization, we have the following steps:

Convert the quadratic equation into standard form if necessary, i.e. , where .

Multiply the coefficient of by constant terms, and we get .

Now try to find two numbers whose product is and sum or difference is equal to (coefficient of ).

Factorise the given expression on L.H.S.

Equate each factor equal to zero.

We get the required roots, say , .
Example:
Solve the equation by factorization method.
Solution:
The given equation in standard form is
Multiplying the coefficient of and the constant term, we get
Divide into two parts such that their difference or sum is
Possible factors of

Sum or difference of factors


(not possible)


(not possible)


(not possible)


(possible)

Therefore,
Either or
or
Example:
Solve the equation by factorization method.
Solution:
The given equation in standard form is
Here, the constant term is absent; its factorization is very simple.
Taking common , we get
Either or
or