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Factors of the form (x+a)(x+b)

Consider the expressions and are not of the type

or i.e., they are not perfect squares. Also these expressions also do not fit the type

Therefore, we use the identity

In this type, the coefficient of x is identified as the sum of a and b. The constant term is the product of a and b.
 

Example

Factorise

Solution

If we compare the RHS of identity (IV) with

With ab = 45, a + b = 14, we can obtain the values of a and b.

If ab = 45 it means a and b are factors of 45. Let us try a = 7, b = 7. For these values a + b = 14 and but ab is not 45.
 

Let us try

a = 9, b = 5. For this a + b = 14 adn ab = 45
The factors are

 

Example

Find the factors of

Solution

 

Example

Obtain the factors of

Solution

 

Example

Find the factors of

Solution

Here 2 is common factor of all the terms.





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