Class 8: Factorization – Lecture Notes – ICSE / ISC / CBSE Mathematics Portal for K12 Students

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:

$(x^2-25)=(x-5)(x+5)$ or

$x^2+9+6x=(x+3)(x+3)$

H.C.F of Monomials

H.C.F of Monomials $= ($ H.C.F. of numerical coefficient $) \times ($ H.C.F. of Literal coefficient $)$

Example:

$6xy^3$ and $9x^2 y^2 = ($ H.C.F of $6$ and $9) \times ($ H.C.F. of $xy^3$ and $x^2 y^2 )= 3xy^2$

Factorization of an expression by taking out the common factor

Case 1

When the expression is in the form of $ax+by$ 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 $6x^2-8xy+4x$

Step 1: Find the HCF of $6x^2, \ 8xy, \ 4x \$ which is $2x$

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

Hence, $6x^2-8xy+4x=2x(6x-4y+2)$

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… $a(x+y) \pm b(x+y)$ . In this case $(x+y)$ is common and we could take that out