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Chapter 2

About Polynomial Equations

 
2.1 Polynomials

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:

The result of the substitution of a number p for x into a polynomial is a number called the value of this polynomial for x=p and is denoted by f(p). If f(p)=0 then
p is called a root p of this polynomial.

Thus, for the polynomials 
we have f( -1 ) = 0, g( i ) = -2, h( 0 ) = 2