1, common factor method: if the first term of the polynomial is negative, the negative sign is extracted first; Every term of a polynomial contains a common factor, so extract this common factor first. Formula method: if the first term of the polynomial is negative, first extract the negative sign; When a whole term of a polynomial is a common factor, put forward this common factor first, and don't leave it out with brackets.

2. Cross multiplication: If the above methods can't be decomposed, you can try to decompose by grouping, splitting and supplementing. Grouping method. Split project method. Supplementary method.

The importance of factorization is as follows:

1, Understanding Mathematical Concepts: Factorization is the basis of understanding mathematical concepts. It helps us to understand the essence of numbers, formulas and equations, and their interrelationships. Through factorization, we can simplify complex mathematical expressions and understand their structures more easily. Simplify the process of solving problems: Factorization can simplify the process of solving mathematical problems.

2. When solving some mathematical problems, we can decompose complex problems into smaller and more manageable parts through factorization. This helps us to better understand the problem and find more effective solutions. Widely used: Factorization has applications in many fields of mathematics and other disciplines.

3. For example, in algebra, factorization is the key to solving equations and inequalities; In geometry, factorization can be used to analyze geometric shapes and measure distances. In physics, factorization is used to solve various complex physical problems. Communication tool: Factorization is an effective communication tool.

In mathematical research, factorization can help us better understand other people's research results and express our own ideas clearly. In mathematics education, factorization is a bridge between students and teachers, which makes teaching more intuitive and easy to understand. Cultivate thinking: Factorization is a way to cultivate logical thinking and abstract thinking.

5. Factorization needs to look at the essence through phenomena, find the internal relationship between numbers or formulas, and use imagination to decompose the problem into different parts. This process helps to improve our thinking ability and problem-solving ability.