1. common factor method: when all terms of a polynomial contain the same factor, this factor can be proposed, and then the remaining parts are added by distribution law to further simplify.

2. cross multiplication: for quadratic polynomial ax? +bx+c, whose factor can be expressed as the product of two linear polynomials. When cross multiplication is used, the product of a and c is decomposed into the product of two factors, then the coefficients of two linear polynomials are determined according to the sign of linear coefficient b, and finally the same terms are merged to get the factors of the original polynomial.

3. Grouping method: when there are four or more terms in a polynomial, and two pairs of terms contain common factors, they can be grouped according to the distribution law, and the common factors are extracted from each group, and then the combination of the same factors is combined into one factor.

4. Total factorization method: For high-order polynomials, we can decompose them into simpler factors by screening relatively simple factors and using techniques such as grouping and cross multiplication.

Data expansion:

A polynomial is transformed into the product of several algebraic expressions in a value domain (real value domain decomposition, that is, all terms are real numbers). The deformation of this formula is called factorization of this polynomial, which is also called factorization of this polynomial.

Factorization is one of the most important identical deformations in middle school mathematics. It is widely used in elementary mathematics, and it is also widely used in finding roots and solving quadratic equations with one variable in mathematics. It is a powerful tool to solve many mathematical problems.

Factorization is flexible and ingenious. Learning these methods and skills is not only necessary to master the content of factorization, but also plays a very unique role in cultivating problem-solving skills and developing thinking ability.

Learning it can not only review the four operations of algebraic expressions, but also lay a good foundation for learning scores; Learning it well can not only cultivate students' ability of observation, thinking development and calculation, but also improve students' ability of comprehensive analysis and problem solving.