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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