Multiplying the crosses can not separate two factors with fractions

This question can actually be divided, as follows:

2x-6)(2x+1)=0

x = 3 or x = -1 2

In addition, in order to facilitate cross multiplication, before using cross multiplication, you should try to reduce the formula to the simplest, such as the problem you said, you can divide both sides of the equation by 2, then it becomes 2x 2-5x-3=0, so that because the two numbers used for cross multiplication are smaller (from 4 to 2, from 6 to 3), so that the combination of splitting is also less, which is more conducive to finding a way to split.

If you really can't find a splitting method for cross multiplication, then you can only use the formula method to solve the solution of the equation through the formula method, such as x1, x2, so that the equation can become in the form of (x-x1) (x-x2) = 0.

In addition, before the cross multiplication, all the coefficients will be turned into integers (for example, x 2 + 4 x + 3 4 = 0 will become 4x 2 + 16x + 3 = 0), and in the case that all the coefficients are integers, it is impossible to divide two factors with fractions, so if there is a situation that cross multiplication cannot be used when doing the problem, don't consider splitting into fractions, just use the formula method to do it.

First of all: the trick of cross multiplication is that it doesn't matter what the constants are.

It's complicated, as long as you can split it into two things m and n, and then try to use cross multiplication, try to decompose the constant term into the form of m*n, and then make m+n equal to the coefficient of the first term (you need to try to make it up) and when the coefficient of the quadratic term is 1, it can be m+n equal to the constant of the first term.

Generally speaking, if you can do it with cross multiplication, you will definitely be able to disassemble it successfully!

For example: x 2-(3a+1)x+2a 2+2a

It is possible to split 2a 2+2a into -2a and -(a+1), and at the same time, 2a-(a+1)=-3a+1), which just satisfies the rule of cross multiplication.

Then, the original equation can be reduced to: (x-2a)(x-a-1)=0

Get: x=2a or x=a+1

Cross multiplication is factorization.

One of the 12 methods, the other eleven are: 1 group decomposition method 2Addition method 3Matching method.

4.Factoring Theorem (Formula Method) 5Commutation method 6Principal Element Law 7Special Value Method 8Pending coefficient method.

9.Double Cross Multiplication 10Quadratic polynomial 11Mention the common factor method.

The method of cross decomposition is simply as follows: the multiplication of the left side of the cross equals the quadratic coefficient.

The right multiplication is equal to the constant term, and the cross-excitation multiplication.

The addition is equal to the primary term coefficient. In fact, it is the use of multiplication formulas.

x+a)(x+b)=x2+(a+b)x+ab.

The decomposition method can be used for the decomposition factor of quadratic trinomials.

It doesn't have to be in the range of integers). For integers like ax2+bx+c=(a1x+c1)(a2x+c2).

The key to this method is to decompose the coefficient of the quadratic term a into the product of the two factors a1 and a2, and the constant term c into the product of the two factors c1 and c2, so that a1c2+a2c1 is exactly equal to the coefficient b of the primary term. Then you can write the result directly: ax2+bx+c=(a1x+c1)(a2x+c2).

When using this method to decompose factors, it is important 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. Basic formula:

x2+(p+q）x+pq=(x+p）(x+q）。

This does not use the cross-macro delay multiplication method to decompose the factor, but uses the method of extracting the common factor to solve the problem. If you want to use cross multiplication, you must simplify the given equation and replace it with a standard one-dimensional quadratic equation in order to apply cross multiplication.

The result in the answer is to make the noisy cong be factored by the square of the extraction of the common factor, and the process is shown in the following figure

x=5 or Qingchun changed the reputation of the judgment pants x=13 3

The factorization of this problem is to extract the common factor (x-5) and then merge the same terms.

3(x-5)²+2(x-5)=0

3(x²-10x+25)+2(x-5)=03x²-30x+75+2x-10=0

3x²-28x+65=0

At this time, Chang Gaixiang can be decomposed by the factor resistance to combat annihilation to obtain:

x-5)(3x-13)=0

This is not a multiplication of crosses, but a common factor.

The common factor is (x-5).

One can mention the common factor (x-5) and deena (x-5) [3 (x-5) + 2} = (x-5) (3x-13) = 0

2. Merge 3x 2-30x+75+2x-10=0

3x 2-28x+65=0, 3x-13)(x-5)=0, x=5 or x=13 Chang Hood Eggplant Chang 3

When the first coefficient is not 1, it is often necessary to try and upgrade the test several times, and it is important to pay attention to the symbols of each coefficient. Lundan's basic formula Liangtong Laozi: x + (p + q) x + pq = (x + p) (x + q) The so-called cross multiplication method is to use the multiplication formula (x+a)(x+b)=x 2+(a+b)x.

Let the integer be the common denominator of the imaginary band of the rational number, and take the integer so that the factorization on the rational number field is reduced to the factorization on the integer ringJust consider decomposing the decomposition into the decomposition of the line.

In factorization, cross multiplication is the inverse of the multiplication formula (x+a)(x+b)=x +(a+b)x+ab.

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

x²-3x+2

Since the sell side is a constant factor, the sum must be equal to the coefficient of the primary term (-1+ -2=-3), because the coefficient of the primary term is -3

If the question is changed to x +3x+2

Then it has to be x 1

x 2 Now you should understand Xiang with hunger! If you don't understand, you're asking! Sincerely.

Good completion (x-1) (x-2) = x -x-2x+2 = x (x-1) -2 (x-1) = (x-1) (x-2) = x -x-2x+2 = x -3x+2

If you follow what you say, you can count celery:

x+1)(x+2)=x +x+2x+2=x Bi Fan +3x+2

Because multiplication is a constant term, the addition is a coefficient of the primary term, and if it is added it is 3 and the middle is -3

The first one cannot be factored because there is no solution to this equation.

The second (3x+7) (x+1).

The third (3x+7) (3x+1).