Factorization: When an algebraic expression can be written as a product of two or more expressions, then each of these expressions is called a factor of the given expression. And the process is called factorization.

Example:

or

H.C.F of Monomials

H.C.F of Monomials H.C.F. of numerical coefficient H.C.F. of Literal coefficient

Example:

and H.C.F of and H.C.F. of and

Factorization of an expression by taking out the common factor

*Case 1*

When the expression is in the form of then proceed as follows:

Step 1: Find the HCF of all the terms of the expression

Step 2: Divide each of the terms with the HCF obtained in step 1

Let’s do an example. Factorize

Step 1: Find the HCF of which is

Step 2: Therefore, is common in all the terms.

Hence,

*Case 2*

In case if a polynomial is a common multiplier of each term of the given expression, then first take the common multiplier and then use distributive law.

Expression would look something like this…. In this case is common and we could take that out

Let’s do one example for Case 2. Factorize:

Factorization of an expression by Grouping the Terms

The expression of the form

Factorizing the difference of two squares

Algebraic expressions like

Factorization of perfect square trinomials

The algebraic expressions of the form

can be factorize using the formula or

Example:

Factorization of Trinomials of the form

In such a case, find two numbers and such that and

Let’s do an example for this as well.

Factorize,

Let and be two numbers

Therefore and . Hence calculating for and we get and . Therefore

Thank you so much for these notes. Very helpful. 😀