# Theory of Equations: Introduction

Variables: In mathematics, a variable is represented by a symbol that can be changed according to the problem. The common symbols used to represent variables are $$x$$, $$y$$, and $$z$$.

Constants: In mathematics, a constant is a fixed and known value that can not be changed, commonly constants are represented by numbers and symbols $$a$$, $$b$$, and $$c$$.

Example: $$2x + y = 25$$

Here $$x$$, and $$y$$ are variables whereas 2 and 25 are constants.

Algebraic Expression: The expression made by using variables and constants with the help of operators (+, -, $$\times$$, $$\div$$) is called an algebraic expression.

Example: $$ax^2 + bx + c$$

Here a, b, and c are constants, and $$x$$ is a variable.

Algebraic Function: An algebraic expression is called an algebraic function of a variable ($$x, y, z$$) and it is commonly represented by $$f(x)$$, $$f(y)$$, $$f(z)$$ etc.

Example: $$f(x) = 2x^2 + 3x + 1$$

Polynomial Expression: It is an algebraic expression with finite terms and for each term, the exponent of the variable should be positive.

Example: $$3x^2 + 2x + 1$$

Here 1, 2, and 3 are constants whereas $$x^2$$ and $$x$$ are variables with positive exponents.

Rational Function: A rational function is the ratio of two polynomials where denominator cannot be zero.

Example: $$f(x) = \frac{x^2 + 2}{x^2 + 1}$$

Here $$x^2 + 1$$ can not be equal to zero.