Cross left multiplication equals quadratic coefficient, right multiplication equals constant term, and cross multiplication plus equals linear coefficient.

Specific steps:

Cross left multiplication equals quadratic coefficient, right multiplication equals constant term, and cross multiplication plus equals linear coefficient.

Extended data:

Principle:

The multiplication formula (x+a)(x+b)=x? +(a+b)x+ab for factorization.

Cross multiplication can factorize the quadratic trinomial (not necessarily in the integer range).

For the shape of the axe? Calculation steps of algebraic expression of+bx+c = (a1x+c1) (a2x+C2):

(1) The quadratic coefficient A is decomposed into two factors a 1 and the product a2 of a 1.

⑵ The constant term c is decomposed into two factors, the product of C 1 and c2, c 1, C2.

(3) Make a 1c2+a2c 1 exactly equal to the coefficient b of the linear term.

(4) result: ax? +bx+c =(a 1x+c 1)(a2x+C2)

Essence: the inverse process of binomial multiplication.

When the first coefficient is not 1, pay attention to the sign of each coefficient. Basic formula: x? +(p+q)x+pq=(x+p)(x+q).