5 X-3=0，X=3/5。

X-2=0，X=2。

Extended data cross multiplication

Factorization method

Cross multiplication is one of the fourteen methods of factorization.

The method of cross multiplication is simply: the product multiplied on the left side of the cross is a quadratic term, the product multiplied on the right side is a constant term, and the cross multiplication and addition are equal to a linear term. The principle is to factorize by using the inverse operation of binomial multiplication. [ 1]

Cross multiplication can be used for factorization of quadratic trinomial (unary quadratic) (not necessarily in integer range). For algebraic expressions like AX2+BX+C = (A 1 x+C 1) (a2x+C2), the key of this method is to decompose the quadratic coefficient A into the product of two factors A1,a2, and the constant term C into two factors C1. Then the result can be written directly: ax2+bx+c = (a1x+c1) (a2x+C2). When using this method to decompose factors, we should pay attention to observation and try to understand that its essence is the inverse process of binomial multiplication.

When the coefficient of the first term is 1, it can be expressed as x2+(p+q) x+pq = (x+p) (x+q); When the first coefficient is not 1, it often needs to be tested many times, so be sure to pay attention to the sign of each coefficient.

Factorization is carried out on the basis of learning four operations of rational numbers and algebraic expressions, which provides a necessary basis for learning fractional operations, solving fractional equations and quadratic equations in one variable, and solving inequality and identity deformation of trigonometric functions in high school. Therefore, factorization is an important content in junior high school mathematics textbooks.

It has extensive basic knowledge functions. Factorization is a good carrier to develop students' intelligence, cultivate their ability and deepen their reverse thinking, because it flexibly and comprehensively uses the basic knowledge of mathematics, has many ways and strong skills, and has a certain depth and breadth for middle school students.

Factorization is very difficult because it has good training ability and thinking function. Today, I mainly talk about a common method in factorization: cross factorization. The factors that can apply this method in junior high school are often seen in the quadratic trinomial.