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.

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

 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) 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 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 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 - 4 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

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