A polynomial is decomposed into the product of several simplest algebraic expressions in a range (such as rational numbers, that is, all terms are rational numbers). This deformation is called factorization, also called factorization. It is widely used in drawing mathematical roots. For example: m? -n？ =(m+n)(m-n)

Principle:

1, the decomposition must be thorough (that is, the factors that can no longer be decomposed after decomposition)

2. Only brackets are left at the end of the result.

3. The first polynomial term of the result is positive. Extract its common factor from the formula, that is

Recombine according to the formula, and then extract the common factor.

4. The first number in brackets cannot be preceded by a negative sign;

5. If the monomial is multiplied by the polynomial, the monomial should be placed before the polynomial. That is the form of a(a+b).

decomposition method

1。 Cross multiplication

The method of cross multiplication is simply: the left multiplication of the cross is equal to the coefficient of quadratic term, the right multiplication is equal to the constant term, and the cross multiplication plus is equal to the coefficient of linear term. In fact, it is to use the multiplication formula (x+a)(x+b)=x? +(a+b)x+ab for factorization.

2. Formula method

1, square difference formula a? -B? =(a+b)(a-b)

2. complete square formula a? 2ab+b？ =(a b)？ There can also be a formula: "the first square, the last square, twice the product of the first and last in the middle."

There are also undetermined coefficient method, binary multiplication, symmetric polynomial, rotational symmetric polynomial method, remainder theorem method and root common factor decomposition method. There is no one-size-fits-all method, and junior high school mathematics textbooks mainly introduce common factor method, formula method and component solution method. There are French division, addition and subtraction, method of substitution, long division, short division, division and so on.