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What is a Polynomial?
Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is defined as an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. Examples of constants, variables and exponents are as follows:

Notation
The polynomial function is denoted by P(x) where x represents the variable. For example,

P(x) = x2-5x+11

If the variable is denoted by a, then the function will be P(a)


Degree of a Polynomial
The degree of a polynomial is defined as the highest exponent of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the largest exponent is called a degree of the polynomial.

Polynomial Degree Example
Zero Polynomial Not Defined 6
Constant 0 P(x) = 6
Linear Polynomial 1 P(x) = 3x+1
Quadratic Polynomial 2 P(x) = 4x2+1x+1
Cubic Polynomial 3 P(x) = 6x3+4x2+3x+1
Quartic Polynomial 4 P(x) = 6x4+3x3+3x2+2x+1
Example: Find the degree of the polynomial P(x) = 6s4+ 3x2+ 5x +19

Solution:

The degree of the polynomial is 4 as the highest power of the variable 4.


Terms of a Polynomial
The terms of polynomials are the parts of the expression that are generally separated by “+” or “-” signs. So, each part of a polynomial in an expression is a term. For example, in a polynomial, say, 2x2 + 5 +4, the number of terms will be 3. The classification of a polynomial is done based on the number of terms in it.

Polynomial Terms Degree
P(x) = x3-2x2+3x+4 x3, -2x2, 3x and 4 3

Types of Polynomials
Depending upon the number of terms, polynomials are divided into the following categories:

Monomial
Binomial
Trinomial
Polynomial containing 4 terms (Quadronomial)
Polynomial containing 5 terms (pentanomial ) and so on …
These polynomials can be combined using addition, subtraction, multiplication, and division but is never divided by a variable. A few examples of Non Polynomials are: 1/x+2, x-3


Monomial
A monomial is an expression which contains only one term. For an expression to be a monomial, the single term should be a non-zero term. A few examples of monomials are:

5x
3
6a4
-3xy

Binomial
A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials. A few examples of binomials are:

– 5x+3,
6a4 + 17x
xy2+xy

Trinomial
A trinomial is an expression which is composed of exactly three terms. A few examples of trinomial expressions are:

– 8a4+2x+7
4x2 + 9x + 7
Types of Polynomials based on Degree
Linear Polynomial

A polynomial whose degree is one is called a linear polynomial.
For example, 2x+1 is a linear polynomial.

Quadratic Polynomial

A polynomial of degree two is called a quadratic polynomial.
For example, 3x2+8x+5 is a quadratic polynomial.

Cubic Polynomial

A polynomial of degree three is called a cubic polynomial.
For example, 2x3+5x2+9x+15 is a cubic polynomial.









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