There are two situations for this method.

① Factorization of x^2 (p q)x pq type formula

The characteristics of this type of quadratic trinomial are: the coefficient of the quadratic term is 1; constant A term is the product of two numbers; a linear term coefficient is the sum of two factors of a constant term. Therefore, we can directly factor some quadratic trinomials whose coefficients are 1: x^2 (p q)x pq=(x p)(x q).

② Factorization of kx^2 mx n-type expression

If k=ac, n=bd, and ad bc=m, then kx^2 mx n=(ax b)(cx d)．

The diagram is as follows:

×

c d

For example: because

1 -3

×

7 2

-3×7=-21, 1×2=2, and 2-21=-19,

So 7x^2-19x-6=(7x 2)(x-3)．

The formula for cross multiplication: decomposition from head to tail, cross multiplication, and summation to find the center

By the way:

Double cross multiplication is a factor A type of decomposition, similar to cross multiplication.

The double cross multiplication method is a binary quadratic hexanomial. The starting formula is as follows:

ax^2 bxy cy^2 dx ey f

x and y are unknown numbers, and the rest are constants

Use an example to illustrate how to use it.

Example: Factoring: x^2 5xy 6y^2 8x 18y 12.

Analysis: This is a quadratic hexanomial, which can be factored using the double cross multiplication method.

Solution: The picture is as follows, just cross-connect all the numbers

x 2y 2

① ② ③

x 3y 6

∴Original formula=(x 2y 2)(x 3y 6)．

The steps of the double cross multiplication method are:

① First use the cross multiplication method to decompose the 2nd degree term, such as x^2 5xy 6y^2= in the cross multiplication diagram ① (x 2y)(x 3y);

②First, calculate the linear coefficient fractional constant term of a letter (such as y). For example, in the cross multiplication diagram ②, 6y? 18y 12=(2y 2)(3y 6);

③ Then press the first coefficient of another letter (such as x) to test, such as the cross multiplication diagram ③ , this step cannot be omitted, otherwise it is easy to make mistakes.

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