The method of proposing the common factor ① Common factor: The common factor contained in each term is called the common factor of each term of this polynomial. (2) Method of proposing common factor: Generally speaking, if every term of a polynomial has a common factor, you can put this common factor in brackets and write the polynomial in the form of factor product. This factorization method is called raising the common factor. The letter AM+BM+cm = m (a+b+c) takes the same letter of each item, and the index of each letter takes the lowest degree. If the first term of a polynomial is negative, a "-"sign is generally put forward to make the coefficient of the first term in brackets positive. Formula method ① Variance formula:. A 2-B 2 = (A+B) (A-B) ② Complete square formula: A 2 2A. Two of them can be written as the sum of squares of two numbers (or formulas), and the other is twice the product of these two numbers (or formulas). Grouping decomposition method: group a polynomial and then factorize it. The grouping decomposition method must have a clear purpose, that is, the common factor can be directly extracted or the formula can be used after grouping. Division and complement: A polynomial is divided. It should be noted that the deformation must be carried out according to the principle of equality with the original polynomial. ※. The general steps of factorization of polynomials are as follows: ① If every term of polynomials has a common factor, then the common factor should be raised first; (2) If there is no common factor, try to decompose it by formula and cross multiplication; (3) If the above methods cannot be decomposed, you can try to decompose by grouping, splitting and adding items; (4) Factorization must be carried out until every polynomial factorization can no longer be decomposed. Matching method: For those polynomials that cannot be formulated, some polynomials can be matched into a completely flat way, and then factorized by the square difference formula. Method of substitution: Sometimes in factorization, you can choose the same part of a polynomial, replace it with another unknown, then factorize it and finally convert it back. Undetermined coefficient method: first, determine the form of factorization factor, then set the letter coefficient of the corresponding algebraic expression, and find out the letter coefficient, thus decomposing polynomial factor.