concept

Monomial (monomial):

1. any algebraic expression in the form of a product of letters and numbers (in division, dividing by a number is equal to multiplying the reciprocal of this number).

2. A letter or number is also called a monomial.

3. The denominator has no letters (the monomial is an algebraic expression, not a fraction).

A, -5, 1x, 2XY and x/2 are all monomials, while 0.5m+n and 2/x are not monomials.

The number of single events refers to the exponential sum of all letter factors in a single event.

This noun was translated into Chinese by Li, a mathematician in Qing Dynasty, according to the concept of the original word.

The monomial is the product of letters and numbers.

Number of times of a monomial: The sum of the indices of all the letters in the monomial is called the number of times of the monomial.

One-way coefficient: the numerical factor in a single item. For example, the coefficient of 2xy is 2; The coefficient of -5zy is -5.

pay attention to

1. Numbers are written before letters, omitting the multiplication sign. [5a、 16xy]

2. The degree of the constant is 0.

3. The denominator of a monomial cannot be a letter. (Otherwise, it is a score, not a single item)

π is a constant, so it can be used as a coefficient.

If the coefficient is a fraction, it should become a false fraction.

5. But when the coefficient of the monomial is 1 or-1, "1" is usually omitted, such as [(- 1)ab] written as [-ab].

Polynomial polynomial

Polynomial A formula consisting of the sum of several monomials is called a polynomial (in subtraction, subtracting a number equals adding its inverse). Each monomial in a polynomial is called a polynomial term, and the highest degree of these monomials is the degree of this polynomial. Items without letters are called constant items. If the degree of the highest term in a formula is 5 and the formula consists of three monomials, it is called a quintic trinomial.

In a broader definition, the sum of 1 or 0 monomials is also a polynomial. According to this definition, polynomials are algebraic expressions. In fact, no theorem is valid only for narrow polynomials, but not for monomials: when 0 is a polynomial, the degree is negative infinity.

Algebraic expressions monomials and polynomials are collectively called algebraic expressions.

A rational expression in algebraic expression. If there is no division or fraction, if there is a division and fraction, but there is no variable in the division or denominator, it is called an algebraic expression. If there is a division operation with letters, then the formula is called fractional decimal. )

Algebraic expressions can be divided into definitions and operations, definitions can be divided into monomials and polynomials, and operations can be divided into addition, subtraction, multiplication and division.

Addition and subtraction involve merging similar items. Multiplication and division include basic operations, rules and formulas. Basic operations can be divided into power operations. Rules can be divided into algebra and division, and formulas can be divided into multiplication formula, zero exponential power and negative integer exponential power.