Math Doubts

Polynomial in a single variable

An expression that represents an unknown quantity mathematically in terms of a single variable is called a polynomial in one variable.

Introduction

in some cases, a single variable is enough to define the indeterminate quantities in mathematical form. Actually, the variable with an exponent is multiplied by a coefficient to represent an unknown quantity. Sometimes, a single expression is sufficient but two or more expressions should be connected by the combination of addition and subtraction in the remaining cases.

A polynomial can be formed by either one or more terms connected by the fundamental operations. Due to the involvement of a single variable in forming the expression, the mathematical expression is called a polynomial in one variable or a polynomial in a single variable.

Variables

Let’s understand the concept of the polynomial in one variable from the following examples.

  1. $4z$
  2. $2y+3$
  3. $7x^2-4x+8$
  4. $5l^3+3l^2+2l-6$

The four expressions are defined in a single variable and the variables are $z$, $y$, $x$ and $l$ respectively. Hence, each mathematical expression is called a polynomial in a single variable.

Constants

Every constant is considered as a polynomial in one variable in mathematics.

  1. $5$
  2. $c$
  3. $4k^3$

In the first case, the number $5$ is a constant. Let us assume that the literals $c$ and $k$ represent two constants. Hence, there is no variable involved in forming the three expressions but they are also considered as a polynomial in a single variable because they can be written with variables as $5x^0$, $cy^0$ and $4k^3z^0$ respectively in mathematics.

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