# Algebraic expressions a single term and a polynomial

## A single term

Definition: a single term is called a finite product of numbers, letters, and their natural degree, and the numbers, letters and their degree.

A single term is zero — the number 0.

Definition: the Degree of a single term is the sum of the letters that is included in a single term. If a single term is a number that is not zero, its degree is considered to be zero.

A single term written in standard form if the first multiplier is a number, called the coefficient of a single term.

— a single term in standard form

Such a single term, if they are equal or differ only in their coefficients.

## Operations on monomials

2. Multiplication
3. Exponentiation
4. Division

## The polynomial

Definition: Polynomial — the sum of a finite number of a single term (each of which is a member of the polynomial).

A single term consisting of one member are also considered polynomials.

The number 0 is called the zero polynomial

### Examples of polynomials

— polynomials

— polynomials consisting of one member

Definition: the Degree of a nonzero polynomial is the greatest degree of the degrees of its members (a single term).

— the polynomial of the third order (because the highest degree is the third)

Polynomial zero (0) degree has not.

## Actions on polynomials

2. Subtraction
3. Multiplication

## Identically equal polynomials

Definition: Two polynomials equal if they acquire runic values for all values of the letters.

## The decomposition of a polynomial into factors

1. The imposition of a common multiplier of the bracket
2. The grouping method
3. The use of formulas of reduced multiplication
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