First, the concept of itemized method
Factorization is a mathematical method of factorization. Its main idea is to split one term in a polynomial into two or more terms, and achieve the purpose of polynomial factorization through group decomposition. This method is widely used in mathematics, especially in algebra and analytic geometry.
Second, the principle of decomposition method
The principle of decomposition method is based on a basic fact: if a polynomial can be decomposed into two or more parts, then the coefficients of these parts must meet certain conditions. By decomposing one term in a polynomial into two or more terms, we can find these parts and determine their coefficients.
Third, the article splitting method.
The general rule of the term splitting method is to split the term that needs to be removed according to the absolute value of the coefficient of the remaining term. If we need to put the polynomial x 2-4x2? Factorization, we can divide it into x 2-2 2x2? 22, so it can be further decomposed into (x+2)(x-2)(x+2)(x? 2)。
Application and solution of decomposition method
I. application in algebraic problems
In algebraic problems, polynomials can be decomposed into simpler forms by decomposition method, which makes it easier to solve problems. For example, we can use decomposition method to convert X 2-4x2? 4 is decomposed into (x+2)(x-2)(x+2)(x? 2), so that the square difference formula can be solved by x 2-4x2? 4 related issues.
Second, the solution of the maximum value of function
Decomposition method can also be used to solve the maximum value of a function. By dividing the function into several parts, we can find the maximum or minimum value of each part, and add or subtract them to get the maximum or minimum value of the whole function. This method is usually much simpler than finding the maximum value of a function directly.
Third, the solution of the root of the equation
Decomposition method can also be used to solve the roots of equations. By dividing the polynomial into two or more parts, we can find the root of each part and add or subtract them to get the root of the whole polynomial. This method is usually much simpler than using trial and error method or Newton iteration method.
Fourth, the application in analytic geometry
In analytic geometry, the intersection of straight lines and curves can be solved by decomposition method to judge whether the points are in a certain area. When a polynomial is divided into two or more parts, the intersection of each part and the coordinate axis can be found, and the intersection of the whole polynomial and the coordinate axis can be obtained by adding or subtracting them. This method is usually much simpler than using simultaneous equations and other methods.