Monomial and polynomial

Algebraic expressions are divided into two groups according to the last algebraic operation indicated.

A monomial is an algebraic expression whose last operation in point of order is neither addition nor¹ subtraction.

Consequently, a monomial is either a separate number represented by a letter or by a figure, e.g. -a, +10, or a product, e.g. ab, (a+b)c, or a quotient, e.g. (a-b)/c, or a power, e.g. b2, but it must never be either a sum or a difference.

If a monomial is a quotient, it is called a fractional monomial; all the other monomials are called integral monomials. Thus, (a-b)/c is a fractional monomial, while (x—y)ab; a(x+y)² are integral monomials.

An algebraic expression which consists of several monomials connected by the + and - signs, is known as a polynomial². Such is for instance, the expression

ab-a+b-10+(a-b)/c.

Terms of a polynomial are separate expressions which form the polynomial by the aid of the + and — signs. Usually, the terms of a polynomial are taken with the signs prefixed to them; for instance, we say: term -a, term +62, and so on. When there is no sign before the first term it is ab or +ab.

A binomial is an algebraic expression of two terms; a trinomial is an expression of three terms and so on.

Notes:

¹ neither...nor – ни…ни

² is known as a polynomial – известен как многочлен, называется многочленом