For example, the coefficient of abc is 1, and the degree is 3.
The literal meaning of coefficient is related numbers. For example, the algebraic expression "3x" represents the product of a constant 3 and an unknown number x, that is, 3 × x, equal to x+x+x. "3x" represents a numerical value, which is only related to x. What is the relationship? "3" means the relationship - the sum of three of its addition. Therefore, "coefficient" can be interpreted as "how many unknowns (sum of addition) [1] 。
The sum of the indices of the unknowns contained in an item is called the number of times of the item.
The term without unknown number is called constant term. For example: 1, 2, 3100, etc. The degree of the constant is 0.
The usage of the word "coefficient" here is different from its original usage, but it can still be borrowed. Assuming that the social relationship to be reflected is 3x=y, x represents the basic situation (population, resources and other facts), and different countries have different situations, 3 represents the number system - the number representing the relationship. By multiplying this, we can get the actual situation of the corresponding country to be outlined, that is, the number y. Of course, whether this can truly reflect the actual social relations is not certain. Math summary.
When discussing mathematical problems derivatives In the relevant expression or equation unknown number Multiplied by a known function or constant It is called coefficient. The term coefficient is also widely used in physics, engineering, computer technology and other fields. For example, the ratio of partial value to total value of a quantity, or some related numbers in the relationship between the change of a quantity and the change of other quantities, are called coefficients. At this time, the coefficient is usually preceded by the proper name of the phenomenon or thing, such as“ Coefficient of expansion "﹑" Carbonic acid coefficient "Etc. monomial Value in factor Also called this Coefficient of monomial 。 [2] polynomial The factor of the highest power term in is called the coefficient of this polynomial. The numerical factor of a single number is its coefficient [3] 。 Formula | coefficient |
14m | fourteen |
123x | one hundred and twenty-three |
The coefficient of 14m in the above table is 14. The coefficient of 123x is 123.
The monomial coefficient in the functional relationship y=x+6 is the same as that in y=x, both of which are 1.
The following points should be noted about the coefficient [4] ：
1. Rational numbers are divided into positive rational numbers, zero, negative rational numbers, integers, and fractions; [5]
2. The term containing letters in the polynomial Integer part Is called the coefficient of the term, and the term without letters is called Constant term 。 For example, in polynomial 4ab-5c+6d-7, 4, - 5, and 6 are coefficients of items ab, c, and d containing letters respectively, while - 7 does not contain letters, so it is called a constant term; 3. If there is no number in the formula, the coefficient is 1 or - 1 by default. Example: - x coefficient: - 1; X factor: 1;
4. Times refer to the sum of the indices of all letters in the monomial;
5. The coefficient of fraction, for example: - 3xy ÷ 2 π is - 3 ÷ 2 π;
6. π is a number and should not be mistaken for a letter. For example, the coefficient of 3 π m is 3 π, and the degree is 1. In arithmetic, if 3 π+6+9, the result is 3 π+15, and π does not need to retain two decimal places;
7. In the monomial formula, the coefficient of the letter is 1 by default. Example: The coefficient of a is 1.
