What is a Polynomial?

An expression that represents a quantity in mathematical form is called a polynomial.

Introduction

The meaning of the polynomial is derived from two words “Poly” and “Nomial”.

1. The prefix “Poly” means many.
2. The word “Nomial” means a term.

The meaning of a Polynomial is many terms as per the meanings of both words.

A quantity can be expressed by only a single expression in mathematics, but it is not possible to write every quantity in a single mathematical expression. In that case, two or more expressions are connected to form another mathematical expression by the operations like addition, subtraction and combination of both. An expression can be formed by either one or more connected expressions but every expression that represents an indeterminate quantity is called a polynomial.

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Single expression

In mathematics, a quantity is expressed in mathematical form by multiplying a coefficient with either one or product of more variables having exponents. The quantity in mathematical form is called a mathematical expression.

For example, the quantity $10$ is expressed mathematically by multiplying a numerical coefficient $5$ with the product of square of a variable $x$ and an indeterminate $y$.

$10 \,=\, 5x^2y$

The quantity $10$ is written mathematically as $5x^2y$ and the quantity in mathematical form $5x^2y$ is called a mathematical expression.

Connecting many expressions

The quantities can be expressed in a single mathematical expression in some cases but it is not possible in the remaining cases. Hence, either two or more mathematical expressions are connected by the mathematical operations like addition or subtraction or combination of both.

For example, the quantity $13$ cannot be expressed in mathematical form by a single expression. Hence, it can be expressed by connecting two expressions $x^2$ and $3y$ by a plus sign.

$13 \,=\, x^2+3y$

The quantity $-3$ cannot be written in mathematical form by a single expression but it can be obtained by connecting the expression $x^2$ with another $3xy$ by a minus sign and another expression $7$ by a plus sign.

$-3 \,=\, x^3-3xy+7$

In this case, the quantities $13$ and $-3$ are expressed in mathematical form as $x^2+3y$ and $x^3-3xy+7$ respectively.

In this case, $x = 2$ and $y = 3$.

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