Algebraic Expressions

Constants

A symbol having a fixed numerical value is called a constant.

Example : 3 - 5, , p etc.

Variable

A symbol or alphabet which takes on various numerical values is known as variable.

Example : Circumference of a circle C = 2p r

Where r - radius of the circle2,

p - constants

C, r - variables

Algebraic Expressions

A symbol or alphabet which takes on various numerical values is known as variable.

Terms : The several parts of the expression separated by + or - sign are called the terms of the expression.

Example : is an expression containing four terms. They are 2, 5x, -8x2y and
.

Example

Mr. Sharma having 2 pencils, 5 pens then form a algebraic expression to express this information.

Solution

Let us denote number of pencils by the variable x and number of pens by the variable y. Then the algebraic expression is 2x + 5y.

Polynomials

An algebraic expression in which the variables involved have only non-negative integral powers is called a polynomial.

Example :
(i) is a polynomial in one variable x.

(ii) is a polynomial in two variables x & y.

(iii) is not a polynomial. is not a non-negative integer.

(iv) is not a polynomial. - 8 is not a non-negative integer.