Polynomial Basics

 Poly means “many” and -nomials means “terms”. 

We can define a polynomial as an algebraic expression with many terms written together using addition, subtraction and multiplication and non negative integer exponents.

  
Some examples of polynomials are given below:    

• 2
• 2x
• 2xyz
• 3x + 7
• x² - y²
• 4x³ - 4xy – 3x + 2

Basic terminology associated with polynomials:

Variables: The unknown quantities which can be known under different conditions and can have difference values depending upon the conditions.  
For example; number of cars in a mall's parking lot, is a variable as it keeps on changing every moment.   
We use alphabet letters like “x” or “y” to represent variables.  
 
Coefficients: Numbers multiplying to the variables in a polynomial are called coefficients.   
For example; in polynomial 3x + 7 the coefficient of “x” is 3.  
 

Terms: Terms in a polynomial are separated by plus or minus signs (keep in mind that we keep the negative sign with each term).   
All the polynomials are made up of terms.  
For example; polynomial 3x - 7 has two terms: “3x” is the first term and “-7” is the second term.  
 
Degree: Degree of a polynomial is the degree of term with the highest exponent.  
For example; Degree of 4x³ - 4xy – 3x + 2 is 3.  
 
Constant Term: Term in a polynomial without a variable is called the constant term.   
For example; 4x³ - 4xy – 3x + 2 has 2 as the constant term.  
 
Monomial: A polynomial with only one term is called a monomial. Mono means “one” and mial means “term”.   
All the rational numbers are monomials.   
For example; 2 is a monomial. 2x, -4xy and 5xyz are some more examples of monomials.  
 
Binomial: A polynomial with two unlike terms is called a binomial. Bi means “two” and mial means “term”.   
For example; 3x – 5 is a binomial. x² - y² is another example of a binomial.  
 
Trinomial: A polynomial with three unlike terms is called a trinomial.   
For example; 2x – 3y + 7 is a trinomial.