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**

**Monomial**- Polynomial with one term, like 3x, 7y**Binomial**- Polynomial with two terms, like 3x + 5**Trinomial**- Polynomial with three terms, like 4x^{2}+ 9x + 7

**Classification on the basis of degree**

**Constant polynomial -**Polynomial of degree 0, like 4, 3**Linear polynomial -**Polynomial of degree 1, like 4x + 9, 5y**Quadratic polynomial -**Polynomial of degree 2, like $2x^{2}-3x+1$**Cubic polynomial -**Polynomial of degree 3, like $x^{3}-2x^{2}-x+1$**Bi quadratic polynomial -**Polynomial of degree 4, like $u^{4}-4u^{3}+9u-\frac{2}{3}$

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