1. Factorization-turning a polynomial into the product of several algebraic expressions is called factorization of this polynomial, which is also called factorization of this polynomial.

2. Factorization method

Extraction method of (1) common factor-If every term of a polynomial has a common factor, you can put this common factor outside the brackets and write the polynomial in the form of factor product. This method of decomposing factors is called extracting common factors.

Extracting common factor is the most basic and commonly used method of factorization, and its theoretical basis is the distribution law of multiplication. Finding the common factor of polynomial term is the key of this method, so we should pay attention to the habit of extracting the common factor first.

(2) Using the formula method-if the multiplication formula is reversed, it can be used to factorize some polynomials. This factorization method is called using formula method.

① Variance formula: A2-B2 = (a+b) (a-b)

② Complete square formula: a2+2ab+b2=(a+b)2.

a2-2ab+b2=(a-b)2

③ Cubic sum formula: A3+B3 = (A+B) (A2-AB+B2)

Cubic difference formula: A3-B3 = (a-b) (A2+AB+B2)

(3) Grouping decomposition method-The method of grouping factors is called grouping decomposition method.

In a decomposed polynomial, if the number of terms exceeds three, the method of factorization is usually group factorization. Generally speaking, there are two kinds of factorization of groups: the first is that each group has a common factor after grouping, which can be further extracted for factorization; The second is that it can be decomposed by formula after grouping.

(4) Cross product-By drawing the cross line decomposition coefficient, the quadratic trinomial factorization method is called cross product.

3. The general steps of factorization

(1) If every term of the polynomial has a common factor, the common factor should be extracted first;

(2) If every term of a polynomial has no common factor, consider whether it can be decomposed by a formula;

(3) For factorization of quadratic trinomial, cross multiplication factorization can be considered;

(4) For polynomials with more than three terms, the group decomposition method should generally be considered.

When factoring, we should choose which method to use according to the form and characteristics of the topic. The above four methods are interrelated. No type of polynomial can only be decomposed into factors in one way, and it is necessary to learn to analyze specific problems.

When we do problems, we can refer to the following formula:

First extract the common factor, then consider the formula;

Try cross multiplication, and the grouping should be appropriate;

Four methods are tried repeatedly, and the last one must be multiplication.