2a/2 b squared minus 4ac.

Quadratic trinomial is a common problem in factorization.

For quadratic trinomial, if the constant term b can be decomposed into the product of p and q, and p+q=a, then =. This is the factorization of cross product.

The following example illustrates how to decompose a factor.

Example 1, factorization.

Analysis: Because

7x + (-8x) =-x

Solution: Original formula =(x+7)(x-8)

Example 2, factorization.

Analysis: Because

-2x+(-8x)=- 10x

Solution: Original formula =(x-2)(x-8)

Example 3, factorization.

Analysis: Although the quadratic coefficient of this problem is not 1, it can also be factorized by cross multiplication.

because

9y + 10y= 19y

Solution: Original formula =(2y+3)(3y+5)

Example 4, factorization.

Analysis: Because

2 1x + (- 18x)=3x

Solution: Original formula =(2x+3)(7x-9)

Example 5, factorization.

Analysis: This problem can be factorized by taking (x+2) as a whole.

because

-25(x+2)+[-4(x+2)]= -29(x+2)

Solution: Original formula =[2(x+2)-5][5(x+2)-2]

=(2x- 1)(5x+8)

Example 6, factorization.

Analysis: This problem can be solved by cross product decomposition as a whole, and then a cross product is applied.

because

-2+[- 12]=- 14 a+(-2a)=-a 3a+(-4a)=-a

Solution: Original formula =[-2][-12]

=(a+ 1)(a-2)(a+3)(a-4)

As can be seen from the above example, cross multiplication is very convenient for factorization of quadratic trinomial.