So a

_{n}x

^{n}+ a

_{n-1}x

^{n-1}+ ...........+ a

_{2}x

^{2}+ ax + a

_{0}= 0,

In this given polynomial form x is a variable and a

_{n}, a

_{n-1}, ….. a

_{2,}a

_{1,}a

_{0}are constants. Here ‘n’ should be positive integer and ‘a

_{n}’ should not be zero. Let’s take an example of polynomial equations

x

^{3}+ 7x

^{2}+ 3x – 2 =0,

Here we can easily see that highest degree of ‘x’ is 3 and all the exponents’ term is non negative integer value. Polynomial equations are categorized according to the degree of Polynomials. So if we are talking about first degree than equation

ax + b =0,

Where ‘a’, ‘b’ are co-efficient and ‘x‘is variable. In Second degree the highest degree of variable x is 2 that’s why we also called them Quadratic Equation. Let’s take an example of quadratic equation

2x

^{2}+ 5x + 3 = 0

this is a polynomial equation to solve polynomial equations it is very necessary to find common factors and the isolation of variable x. so here we can see that in quadratic form equation 5x is the single term which is in 1 degree now we have to separate that term like that, addition will become 5x and multiplication will become 6x

^{2}. In short we have to find factors. We get two prime factors while separating 5x which is 2 and 3 so we can rewrite that equation like

2x

^{2}+ 2x + 3x + 3 = 0

Now we take 2 and 3 common in terms 2x

^{2}+ 2 and 3x +3,

2x (x + 2) + 3 (x + 1) = 0

After that we separate common term (x + 2) and join both factors together,

(x + 2) (2x + 3) = 0,

So (x + 2) = 0 and (2x + 3) = 0,

Do now the values of ‘x’ are,

x = -2 and x = -3 / 2.