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.
H.C.F of Monomials
H.C.F of Monomials= (H.C.F. of numerical coefficient) × (H.C.F. of Literal coefficient)
Let’s do an example:
Factorization of an expression by taking out the common factor
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
Step 2: Therefore, is common in all the terms.
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
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.
Let and be two numbers
calculating for and we get and