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