(1) common factor: the common factor of each term is called ~ of this polynomial term.

② Extraction method of common factor: Generally speaking, if every term of a polynomial has a common factor, you can put this common factor outside brackets and write the polynomial as a factor product. This method of decomposing factors is called extracting common factors.

am+bm+cm=m(a+b+c)

③ Specific methods: When all the coefficients are integers, the coefficients of the common factor formula should take the greatest common divisor of all the coefficients; The letter takes the same letter for each item, and the index of each letter takes the lowest degree. If the first term of a polynomial is negative, a "-"sign is usually put forward to make the coefficient of the first term in brackets positive.

(2) Using the formula method

① variance formula:. a 2-b 2 = (a+b) (a-b)

② Complete square formula: a 2 2ab+b 2 = (a b) 2.

Polynomials that can be decomposed by the complete square formula must be trinomials, two of which 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). ※ 。

(3) Grouping decomposition method

Grouping decomposition: a method of grouping polynomials and then decomposing factors.

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.

(4) Methods of splitting projects and supplementing projects

Decomposition and supplement method: one term of polynomial is decomposed or filled with two terms (or several terms) which are opposite to each other, so that the original formula is applicable to common factor method, formula method or group decomposition method; Note that it must be the same as the original polynomial.

The principle of deformation.

General steps of polynomial decomposition. ※:

(1) If the polynomial term 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.

(5) 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.

(6) Substitution method: Sometimes in factorization, you can choose the same part of the polynomial and replace it with another unknown, then factorize it and finally convert it back.

(7) undetermined coefficient method: firstly, determine the form of factorization factor, and then set the letter coefficient of the corresponding algebraic expression to find out the letter coefficient, thus decomposing the polynomial factor.