Factorization and cross multiplication in junior high school mathematics.

Hehe, I can't find my notes. Tell me what I remember. sorry a^2+(p+q)a+p*q=(a+p)(a+q)

Here, P and Q are numbers, which is a simple crossover method and a coincidence (his quadratic coefficient is exactly 1). If this kind of formula cannot be factorized [a 2+(p+q) a+p * q]

You can look at its constant first, which is completely a number. It is obtained by multiplying two numbers. You can take this number apart and multiply it by something. Then add these two numbers, and if they are exactly equal to the linear term (that is, (P+Q)a in the formula).

The coefficient of this term), then your two constants are found right, and then directly brought into the following formula [(a+p)(a+q) A is the letter.

P and q are constants. For example: a 2-7a+ 12

12 can be divided into: 1* 12.

2*6

4*3

Or (-1)*(- 12) (

-2)*(-6) (-3)*(-4)

[It should be noted here that the multiplication of two negative numbers is also positive, so it is more important to consider] Finally, the results of adding two numbers in each group are compared, and it is found that (-3)+(-4) is exactly the coefficient of a linear term -7.

. So this formula can be decomposed into [a+(-3)]*[a+(-4)].

Namely (a-3)*(a-4)