# Polynomials

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