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# Polynomial

The word "polynomial" is made up of two words - "poly" and "nomial". Poly means "many" and nomial means "terms". So, etymologically, polynomial means one which contains many terms. A polynomial is a mathematical expression which is made up of many terms formed by variables and constants conjoined together with the help of algebraic operators - addition or subtraction.

More specifically, a polynomial is a mathematical expression of the form: is known as a polynomial of degree n, provided that $a_{n}\neq 0$.

$a_{0},\ a_{1},\ a_{2},\ ....,\ a_{n}$ are constants and 'n' must be a non-negative integer.
For such mathematical expression to be categorized as polynomial, exponent of the variable must be non negative integer.For Example: $x^{3}+x^{2}-3x-1$ and $3u-5$ are polynomials.
but $\sqrt{x}+x-1$ and $y^{2}-y^{-\frac{3}{2}}+7$ can not be categorized as polynomials.

Degree of a polynomial
Degree of a polynomial is defined as the highest exponent of variable in a polynomial.
For example: $x^{3}-x^{2}+3x-1$ is a polynomial of degree 3 and 4x - 5 is a polynomial of degree 1.

Types of polynomials
Polynomial can be classified on the basis of following:

• Classification on the basis of number of terms
1. Monomial - Polynomial with one term, like 3x, 7y
2. Binomial - Polynomial with two terms, like 3x + 5
3. Trinomial - Polynomial with three terms, like 4x2 + 9x + 7
• Classification on the basis of degree
1. Constant polynomial - Polynomial of degree 0, like 4, 3
2. Linear polynomial - Polynomial of degree 1, like 4x + 9, 5y
3. Quadratic polynomial - Polynomial of degree 2, like $2x^{2}-3x+1$
4. Cubic polynomial - Polynomial of degree 3, like $x^{3}-2x^{2}-x+1$
5. Bi quadratic  polynomial - Polynomial of degree 4, like $u^{4}-4u^{3}+9u-\frac{2}{3}$

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