**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

2x^{7} – 5xy + 3y + 12 (** x, y are variables and 2, 5, 3 & 12 are constants**)

xy^{3}z + 37x – 100 (*x, y, z are variables and *** , 37 & – 100 are constants**]

__Polynomials__

An algebraic expression is said to be polynomial if and only

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

For example – **2x ^{7} – 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, 2x^{7} – 5xy + 3y + 12 is a polynomial

*[Note: Fourth term of the polynomial is 12 which can be written as 12 = 12 **× 1 = 12x ^{0} *

* {x ^{0} = 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: –3x^{4}, 28p^{2}q 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: 3x^{4} + 3 and 28p^{2}q –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: 3x^{4} + 3 + 28p^{2}q 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: 3x^{4} + 3 – 28p^{2}q –100y, etc is a Quadrinomial.*

[Note: The word **Poly** means ** many**]

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