Pascal factorized cross multiplication

Doesn't that make sense.

The cross multiplication mantra is as follows:Cross normal factoring: first split the coefficient of the quadratic term into the form of two products, and then split the constant term into two products of the form of the key is unknown, and then the cross product is equal to the coefficient of the primary term.

1. Extracting the common factor method.

2. Formula method (squared difference formula and perfect squared formula).

For example: matching method and cross method, etc.

x+2y)(2x-11y)=2x2-7xy-22y2。

x-3)(2x+1)=2x2-5x-3。

2y-3)(-11y+1)=-22y2+35y-3。

This is known as double cross multiplication.

Method formula for cross multiplication: Manuscript elimination.

The left side of the cross is multiplied equally, the right side is multiplied equals the constant term, and the cross multiplication is added to the primary term coefficient.

Usefulness of cross multiplication:

1) Use cross multiplication to break down the factor.

2) Use cross multiplication to solve a quadratic equation.

Advantages of the multiplication method of ten cha rolling words:

Using cross multiplication to solve problems is relatively fast, can save time, and the use of arithmetic is not large, and it is not easy to make mistakes.

Write (x+a)(x+b) as x 2+(a+b)x+ab, that is, (x+a)(x+b) x 2+(a+b)x+ab, and write the above equation in reverse.

x 2+(a+b)x+ab (x+a)(x+b) is actually to divide the coefficient of the primary term and the constant term of the quadratic trinomial formula into the sum of the sum of the two numbers, that is, the coefficient of the primary term is divided into the sum of the two numbers, a+b

The constant term is divided into the product of two numbers.

ab is written as 1a

1b The first column is the two factors of the coefficient of the quadratic term.

The second column is the two factors of the constant term.

Cross-multiplication and then addition should be the coefficient of the primary term.

Try all three of these things correctly, the first line will decompose the first factor of the cause, and the second line will decompose the second factor of the cause.

Try a few more times and you'll be proficient.

Cross multiplication can factor certain quadratic trinomials ax2+bx+c(a≠0). The key to this method is to decompose the coefficient a of the quadratic term into the product of two factors a1 and a2, and decompose the constant term c into the product of two factors c1 and c2, and make a1c2+a2c1 exactly the coefficient of the first term b, then it can be directly written as the result: ax2+bx+c=(a1x+c1)(a2x+c2), when using this method to decompose the factor, we should pay attention to observe, try, and realize that it is essentially the inverse process of binomial multiplication.

When the first coefficient is not 1, it often takes several tests, and it is important to pay attention to the symbols of each coefficient.

Example: x2+2x-15

Analysis: The constant term (-15) <0 can be decomposed into the product of two numbers with different signs, which can be decomposed into (-1) (15), or (1) (-15) or (3).

5) or (-3) (5), where only the sum of -3 and 5 in (-3) (5) is 2.

x-3）（x+5)

The method of cross decomposition is simply as follows: the left side of the cross is multiplied equals the quadratic term, the right side multiplied is equal to the constant term, and the cross multiplication and addition is equal to the primary term.

For a polynomial of the shape ax2+bx+c, δ=b2-4ac can be used to determine whether it can be factored using the cross decomposition method. When the δ is a perfectly squared number, the polynomial can be cross-multiplied in an integer range.

1. The cross decomposition method can be used to decompose the factor of the quadratic trinomial (not necessarily within the range of integers) 2. For integers like ax2+bx+c=(a1x+c1)(a2x+c2), the key to this method is to decompose the quadratic coefficient a into the product of two factors a1 and a2, so that a1c2+a2c1 is exactly equal to the coefficient b of the primary term.