**Algebraic equation**is also known as polynomial equations. A polynomial expression is made up of constants and variable, combined using mathematical operators. When a polynomial expression is equated to some constant value, it becomes polynomial equation. To understand this in simple terms, go through the following example.

x²-5x+6

Is a polynomial equation, here x is a variable, 5 and 6
are constant and mathematical operators used are addition and square, but

x²-5x+6=0 is a polynomial equation or algebraic equation
because it is equated to a constant (in this case zero).

The general form of a polynomial equation is

As one can notice the power f x keep on decreasing. The
above equation is called a polynomial degree of order n.

**What is degree of polynomial?**

Degree of a polynomial is the highest power of variable.
Degree of a polynomial is always a non-negative integer.

Depending upon the degree of polynomial, polynomial may
de defined as quadratic equation, Linear equation or constants.

To be very particular a polynomial equation of degree 2
is called quadratic equation, polynomial equation of degree 1 is called linear
equation and polynomial equation with degree of polynomial zero are nothing but
constants values.

In this module we will focus on quadratic equations

The general form of a polynomial equation is ax²+bx+c= 0

Here,

·
a is the coefficient of x

^{2}
·
b is the coefficient of x And

·
c is the constant term

To solve quadratic
equations there are three methods available, they are:

·
factorization

·
completing the square method

·
using quadratic formula

Let us see each method is detail.

**Factorization method**

In this method the quadratic equation is decomposed into
2 factors. (What are factors? Factors are those values, which if substituted
into the original equation, then it result out to zero. ) for example in our
example, x²-5x+6 =0 the equation can be written in the form, (x-2) (x-3)=0 . If
one opens the bracket and multiply the terms then we get the original equation x²-5x+6
. Therefore (x-2) (x-3) are known as factors of the equation x²-5x+6 =0

**How to find factors of any quadratic equation?**

To find the factors of any quadratic equation, follow
these steps:

**Step 1**Decompose the middle term, i.e., the terms containing the x and it coefficient into 2 parts, such that the product of those two terms should be equivalent to the product of x

^{2}term and the constant term. Also, the summation of those decomposed two terms should give back the original middle term.

**Step 2**Take common out from the first two terms, and from second two terms in such a way, that you get common factor among both these terms.

**Step 3**Again take the common factor out, and then you are left with 2 final factors of the original equation.

If the above mentioned steps are not clear to you, go
through the following steps:

Let’s start with

x²-5x+6 = 0

Now let us write 5x as -2x -3x

x²-2x -3x+6 =0

This is so because, product of (-2x) and (-3x) is (+6x

^{2}), which is same as product of (x^{2}) and (6), i.e., (6x^{2}), the product of x^{2}term and constant term.
Now, take x common out from x

^{2 }and (-2x) and (-3) common out from (-3x) and (6)
The equation becomes x(x-2)-3(x-2)=0

Now take (x-2) common out

(x-2) (x-3)= 0

These are the factors of the original equation x²-5x+6=0

The values of x in this case would be 2 and 3.