Monomials, Binomials, and Polynomials
Topic Index | Algebra Index | Regents Exam Prep Center

Constants like 13 are monomials since they can be written as
  13x0 = 13•1 = 13
where the variable is x0.

Smono1.gif
The ending of these words "nomial" is Greek for "part".

 

  
 
bullet A monomial is the product of non-negative integer powers of variables.  Consequently, a monomial  has NO variable in its denominator.  It has one term.  (mono implies one)
13,    3x,    -57,     x²,     4y²,     -2xy,  or  520x²y²
                 (notice:  no negative exponents, no fractional exponents)
  
 
bullet A binomial is the sum of two monomials.  It has two unlike terms. 
(bi implies two)
3x + 1,    x² - 4x,     2x + y,    or    y - y²

 
bullet A trinomial is the sum of three monomials.  It has three unlike terms.   (tri implies three)
x2 + 2x + 1,      3x² - 4x + 10,       2x + 3y + 2

 
bullet A polynomial is the sum of one or more terms.  (poly implies many)
x2 + 2x,      3x3 + x² + 5x + 6,       4x - 6y + 8

 

Polynomials are in simplest form when they contain no like terms.
              x2 + 2x + 1 + 3x² - 4x  when simplified becomes 4x2 - 2x + 1

 

Polynomials are generally written in descending order.
    Descending:  4x2 - 2x + 1  exponents of variables decrease from left to right