,
where a is a real number and n a positive integer. Every real number is
also called a monomial.
For example the expressions
, 
, 
,
2x and the numbers 2, -3, 0 are all monomials of x.
Let's say that x is a variable that can take any real value.
Definition
A monomial
of x is called every expression of the form ,
where a is a real number and n a positive integer. Every real number is
also called a monomial.
For example the
expressions , , ,
2x and the numbers 2, -3, 0 are all monomials of x.
Definition
A polynomial of x is called any
expression of the form 
where
n is a positive integer and 
.
The monomials 
are
called terms of the polynomial and the numbers
coefficients
of the polynomial. If 
,
the term 
is
called the leading term of the polynomial and the number n degree of the
polynomial. The term 
is
called the constant term of the polynomial.
Polynomials of the form 
,
that is, non zero numbers are called polynomials of degree 0.
A polynomial all of whose coefficients
are equal to 0 is called an identically vanishing polynomial and is replaced
by 0. No degree is attributed to identically vanishing polynomials.
For example:
is
a polynomial of degree 3.
is
a number called the value of this polynomial for x=p and
is denoted by f(p). If f(p)=0 then
Thus, for the polynomials 
, 
, 
we have f( -1 ) = 0, g( i ) = -2, h( 0
) = 2
