What is the factorization of algebra and the cross factorization method, thank you

There are various divisions of factorization.

The cross division is the simplest and most commonly used one.

Factorization has: squared difference formula. Perfectly squared.

Cross decomposition is also one of the methods.

Let's look at the coefficients first, which are respectively and 12, both of which are multiples of 6.

Extract the 6 first.

6(x ²-3x +2)

Then use the multiplication of the cross to decompose it, and you can get it.

6(x -1)(x -2)

f'(x)=6x 2-18x+12=6(x-1)(x-2), let f'(x)=0, gets: x1=1, x2=2

At x<1, f'(x) >0 increments, 12, f'(x) >0 increments

Incrementalintervals (- 1) and (2,+ decreasing intervals (1,2).

The method of factorization is relatively simple in the genus cross multiplication method, and other methods such as extracting common factors, matching methods, formula methods, etc., are used together and are not used separately.

Here's how, please refer to:

6x 18x+12, from which it can be seen that can be divisible by 6, so you can extract 6 to get: 6 (x 3x+2) = 6 (x 2) (x 1) If you are not sure whether it is right or not, you can verify that it will.

6 (x 2) (x 1) multiplied.

See if it's equal to 6x 18x+12

Knowing that f(x) 6x -18x+12 is obtained, the common factor is extracted first, and then the factor is decomposed.

6(x²-3x+2)

6(x-1)(x-2)。

6x²-18x+12

6 (x -3x+2) – extracts the common factor 6

6 (x-1) (x-2) – cross multiplication.

This is the basic knowledge of the first grade of junior high school...

Factorization is a method used in mathematics to solve higher-order unary equations. Put the number on one side of the equation and pass. If the terms of a polynomial have a common factor, you can propose this common factor to make the polynomial two.

6x²-18x+12=6(x²-3x+2)=6(x-2)(x-1)

This factorization is not difficult. In your draft, why is the square of the first item in parentheses missing?

6 for each term is proposed, and then the factors can be factored by cross multiplication.

Extract the common factor 6 first

6 (x-3x+2) multiply the brackets with a cross.

6(x-1)(x-2)

In this problem, the common factor is extracted first, and 6 is proposed. Then we use the cross multiplication method. Two steps in place.

6x^2-18x+12

6(x^2-3x+2)

6(x-1)(x-2)

Each item of this factor has a common factor 6, and the common factor 6 is extracted first, and then the factor can be broken by cross multiplication.

6x²-18x+12

6(x²-3x+2)

6(x-1)(x-2)

Let's start with the common factor.

6, then multiply with crosses.

It is to put the constant term.

2 is divided into (-1) (2) and satisfies (-1) + (2) = coefficient of the primary term -3, so that the polynomial x -3x+2 can be decomposed into the product of two factors (x-1) and (x-2).

You have to be able to observe and analyze. Polynomials that can be factored have this feature in form, the coefficient of a term is the sum of the two constants in the two factors that are finally factored, and the constant term is the product of the constant terms in the two factors. Most.

The reason is unknown, but as before, everything is the same, except for the name change.

The basic formula (x-y) squared = x squared + y squared - 2xy, for example, the first one can be written as (4x) squared + (2y) squared - (2*4x*2y) = (4x-2y) squared.

Solve equations 3x2-7x-1=0 respectivelyx2-4x+2=0 of two a1,a2; b1,b2

I don't count what the root of 3x2-7x-1=(x-a1)(x-a2)x2-4xy+2y2=(x-b1y)(x-b2y) is.

1. |a-2|+b^2-2b+1=|a-2|+(b-1) 2=0, so |a-2|=|b-1|, a-2=b-1-->a=b-3--> hold a-2b=-b-3

Or: a-2=1-b--> a= -b+3-->a-2b=-b+3-2b=-3b+3

2.1 2a 3*b+a 2*b 2+1 macro orange 2a*b 3=1 2ab(a 2+2ab+b 2)=1 2ab(a+b) 2=1 2*2*(2) 2=4

3.Original formula = 3 (m 4-2m 2 + 1) = 3 (m 2-1) 2

The solution of the equation 2x squared - 2x-1 2=0 is used to find the root formula, that is, x1 and x2 generations a(x-x1) (x-x2);

Treat x square + 6xy + 3y square = 0 as a quadratic equation about x, and treat y as a constant, and use a solution similar to the one above. Namely.

2x squared - 2x-1 2 = 2[x-(1+2 1 2) 2][x-(1-2 1 2) 2].

x square + 6xy + 3y square = [x-(-3+6 1 2)y][x-(-3-6 1 2)y].

The rest of the two are the same way.

1 Answer: The square of (x-y) - 8 (x-y) + 16 = 0, that is, the square of (x-y-4) = 0

The solution is x-y=4

2 Answer: the square of a b + the square of a + the square of b + 1-2ab-2ab=0, that is, the square of (ab-1) + the square of (a-b) = 0, so we get ab=1 a=b, so a=b=1, so a=b=1

So the square of a + the square of b = 2

1A: x 2 + y 2-2xy-8x+8y+16=(x-y) 2-8(x-y)+16=(x-y-4) 2

2 Answer: a 2b 2+a 2+b 2+1=4aba 2b 2-2ab+1+a 2-2ab+b 2=0(ab-1) 2+(a-b) 2=0

The sum of two non-negative numbers is 0, and both non-negative numbers are 0

So: ab-1=0;a-b=0；So ab=1so: a 2 + b 2 = (a-b) 2 + 2 ab = 2

<> detailed steps are written on the paper slag, and I guess that the line is quiet.