We will now study what a polynomial is, how to calculate its numerical value, perform arithmetic operations, among other subjects on this important mathematical content.

## Definition

We call it **polynomial function** or simply, **polynomial** the function defined by:

On what:

- , with
**no**

are the terms of the polynomial (note that all exponents must be natural numbers); - are real numbers called coefficients;
- is the independent term of
**x**; **x**is the variable.

## Degree of a polynomial

The degree of a polynomial is the maximum exponent it has. If then the maximum exponent **no** is said degree of the polynomial and we indicate **gr (P) = n**.

**Examples**

**P (x) = 5**or**P (x) = 5xº**it is a**constant polynomial**, that is,**gr (P) = 0**.**P (x) = 3x + 5**it is a**1st degree polynomial**, this is,**gr (P) = 1**.**P (x) = 4x³ + 7x²**it is a**3rd degree polynomial**, that is,**gr (P) = 3**

**Note: **If **P (x) = 0**, the degree of the polynomial is not defined.

## Numeric value

The numeric value of a polynomial **P (x)**, for **x = a**, is the number obtained by substituting **x **per **The** and performing all operations indicated by the relation that defines the polynomial.

**Example**

Consider the polynomial :

Next: Root of a Polynomial