Analytical analysis example of cross multiplication: first decompose the quadratic term coefficient and write it in the upper left corner and the lower left corner of the crosshair, then decompose the constant term and divide the points.

Don't write it in the upper right corner and lower right corner of the crosshair, and then cross multiply to find the algebraic sum to make it equal to the coefficient of the first term.

Decomposition of quadratic coefficient (only take positive factor, because the result of negative factor is the same as that of positive factor.

2= 1×2=2× 1;

Decomposition of constant term:

3= 1×3=3× 1=(-3)×(- 1)=(- 1)×(-3)

Draw a cross line to represent the following four situations:

1 1

╳

2 3

1×3+2× 1=5 ≠-7

1 3

╳

2 1

1× 1+2×3=7 ≠-7

1 - 1

╳

2 -3

1×(-3)+2×(- 1)=-5 ≠-7

1 -3

╳

2 - 1

1×(- 1)+2×(-3)=-7

Through observation, the example analysis of cross multiplication shows that the fourth case is correct, because after cross multiplication, the sum of two algebras is exactly equal to the coefficient of the first term -7.

Solution 2x? -7x+3=(x-3)(2x- 1)

Usually, for quadratic trinomial ax? +bx+c(a≠0), if the quadratic coefficient a can be decomposed into the product of two factors, namely a=a 1a2, then the constant term c can be decomposed into the product of two factors, namely c=c 1c2, and a 1, a2, c/kl.

a 1 c 1

╳

a2 c2

a 1c2 + a2c 1

Cross-multiply and add diagonally to get a 1c2+a2c 1. If it is exactly equal to the quadratic trinomial ax? The linear coefficient b of +bx+c is a 1c2+a2c 1=b, then the quadratic trinomial can be decomposed into the product of two factors a 1x+c 1 and a2x+c2, namely

ax^2+bx+c=(a 1x+c 1)(a2x+c2)

This method of decomposing quadratic trinomial by drawing cross lines is usually called cross multiplication.

Example 2