Let's say that x is a variable that can take any real value.
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.
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.
Thus, for the polynomials , ,
we have f( -1 ) = 0, g( i ) = -2, h( 0 ) = 2