Factorization

Decomposition of polynomial into two more factors is called factorization. It is usually done in algebra as well in numbers. For example the factorization of polynomial x2 − 4 is as (x − 2)(x + 2). It is pertinent to mention here that final answer obtained through factorization is always in product shape.

The basic theme for which the factorization is done is that the provided polynomial has to be reduced into basic building blocks or into irreducible polynomials. Some time fundamental theorem is also used in order to factoring the polynomial. The terminology used as opposite of polynomial factorization is called expansion. The final answer obtained through expansion is always got in the shape of sum of terms. When we will use fundamental theorem, every positive integer greater than one has a unique prime factorization. I will make factorization with the following methods with the help of vidos:-


(a) By taking common

(b) By mid term break method

(c) By applying formula
Factors are numbers we can multiply together to get another number:

Example: 2 and 3 are factors of 6, because 2 × 3 = 6.


A number can have MANY factors!

Example: What are the factors of 12?
3 and 4 are factors of 12, because 3 × 4 = 12.
Also 2 × 6 = 12 so 2 and 6 are also factors of 12.
And 1 × 12 = 12 so 1 and 12 are factors of 12 as well.

So 1, 2, 3, 4, 6 and 12 are all factors of 12
And -1, -2, -3, -4, -6 and -12 also, because multiplying negatives makes a positive.



In Algebra, factors are what we can multiply together to get an expression.
(x+3) and (x+1) are factors of x2 + 4x + 3:

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