# Algebraic Expression | Basic | Algebraic Expression Example

## Algebraic Expression | Basic | Algebraic Expression

A mathematical expression that exists in the form of variables and constants along with mathematical operations viz., addition, operation, multiplication and division is called algebraic expression. For example

2x7 – 5xy + 3y + 12 (x, y are variables and 2, 5, 3 & 12 are constants)

xy3z + 37x – 100 (x, y, z are variables and  , 37 & – 100 are constants]

Polynomials

An algebraic expression is said to be polynomial if and only

1. Coefficients are real numbers (Natural Number, Whole Number, Integers & Rational Numbers)
2. Exponents in each terms of the variable are non-negative integers.

For example – 2x7 – 5xy + 3y + 12

Here the coefficients are 2, 5, 3 and 12 are real numbers

& exponents are 7, 1 and 0 are non- negative integers

(Exponents of the variable x are 7, 1 & 0 and exponent of y is 1. All these are non-negative integers)

Hence, 2x7 – 5xy + 3y + 12 is a polynomial

[Note: Fourth term of the polynomial is 12 which can be written as 12 = 12 × 1 = 12x0

{x0 = 1} and so exponent of x is 0]

Let us take another example which seems to be polynomial but it is actually not a polynomial.

x + 5y + 10 is not a polynomial because exponent of x is  and it is not an Integer. ## Various forms of Polynomials

Monomial: The word MONO Means 1(One). So, any polynomial having only 1(One) Term is refer to as Monomial.  For example:  –3x4, 28p2q and –100, etc are Monomials.

Binomial: The word Bi means 2(Two). So, any polynomial having only 2(Two) Terms is refer to as Binomial.  For example: 3x4 + 3 and 28p2q –100, etc are Binomials.

Trinomial: The word Tri means 3(Three). So, any polynomial having only 3(Two) Terms is refer to as Trinomial.  For example: 3x4 + 3 + 28p2q is a Trinomial.

Quadrinomial: The word Quadri means 4(Four). So, any polynomial having only 4(Four) Terms is refer to as Quadrinomial.  For example:  3x4 + 3 – 28p2q –100y, etc is a Quadrinomial.

[Note: The word Poly means many]

How to express Decimal Number as Rational Number?