It is always better
to start from scratch and know how the process in-built together and
incorporated at places than to start working and return back to the basics.

**What does the term Factorization mean?**

It is the process of
finding out factors of a polynomial or any
equation. It is moreover like splitting of a
complex term into two other numbers whose multiplication product if
equal to the main term.

It can also be defined
as the decomposition of a mathematical equation and is not
necessarily applicable to polynomials, but also for Matrices and numbers

**Why should one Factorize?**

The main objective of factorizing is
to reduce the complexity of the problem. The end results of
Factorizing are something which cannot be further divided, thus breaking the
equation to its simpler form.

The factorizing terms in
their form can further be multiplied again to retain the original
equations. This is also known as the expansion
of polynomials. It is the best way to verify the solutions obtained after the
factorizing process.

Equation |

**When should we Factorize?**

Before moving on to
factorization let us have a look at the factor theorem:

The factor theorem
states that when a polynomial f(x) has a factor
that is (x-k), it is only when f(x)=0

This means that the
value of k that is obtained is a root of the polynomial.

**Other uses of the Factor theorem are:**

The factor theorem
is used to remove known zeros from a polynomial while leaving all unknown zeros
fixed, thus producing a lower degree polynomial whose zeros are easier to solve.

The
method is:

1. Use the factor
theorem to conclude that the term (x-a) is
a factor of f(x).

2. Solve the
polynomial g(x) =f(x)/f(x-a), for example using Long
Division method of Polynomials or Synthetic Division method.

3. Say that any
root x is not equal to an of f(x)
=0 is a root of g(x)=0.

4. Since the polynomial
degree of g is one less than that of the degree of f, it is "simpler" to find the
remaining zeros.

**Few Common Methods of Factorization**

Listed below are the few
commonly used methods for factorization:

Let us have a quick look
at them

**1. Highest Common Factor**

The highest common factor of algebraic expressions is
useful in factorization; and it is the product of the common prime factors,
which includes both common numerical and algebraic factors.

**2. Using the Common factor**

ab+bc= b(a+c)

**3. Using the Difference of the square formula**

a^2-b^2= (a+b)(a-b)

By using the above method, you can easily find the factors of a
number.

**Real Life applications of Factorization**

**Finance**

Commonly used in finance
and accounting where the present value of the assets are determined and for
stock evaluation. Its uses are also traced in bond trading and calculations.

**Numerical Analysis**

For complex and high
ordered equations in derivations and formulae method of factorization is needed
to reduce the complexity of the problem, thus getting a valid
solution or a better and simpler form of the equation. Also, high
tech algorithms use the basics of Factorizing.

**Quadratic equations**

Integration sums and
wave equations always end up unexpectedly in a quadratic form and then the only factorization can reach for your help. It
is also widely used for solving numerical and calculation unknown values when
in higher than or equal to 2nd order format.