What is the learning method of factorization? How to learn? Headache...

The theorems in the textbook, you can try to reason by yourself. This will not only improve your proof ability, but also deepen your understanding of the formula. There are also a lot of practice questions.

Basically, after each class, you have to do the questions of the after-class exercises (excluding the teacher's homework). The improvement of mathematics scores and the mastery of mathematical methods are inseparable from the good study habits of students, so good mathematics learning habits include: listening, reading, homework, listening:

You should grasp the main contradictions and problems in the lecture, think synchronously with the teacher's explanation as much as possible when listening to the lecture, and take notes if necessary After each class, you should think deeply and summarize, so that you can get one lesson and one Reading: When reading, you should carefully scrutinize, understand and understand every concept, theorem and law, and learn together with similar reference books for example problems, learn from others, increase knowledge, and develop thinking **: Learn to think, explore some new methods after solving problems, and learn to think about problems from different angles, or even change the conditions or conclusions to discover new problems, after a period of study, you should sort out your own thinking to form your own thinking rules Homework:

In short, in the process of learning mathematics, we should realize the importance of mathematics, give full play to our subjective initiative, pay attention to small details, develop good mathematics learning habits, and then cultivate the ability to think about problems, analyze problems and solve problems, and finally learn mathematics well

Give you a PPT and you will be able to take a look at it recently and study it. The learning method is to focus more on the topic.

1. Mention the common factor method.

The common factors that are contained in the terms of several polynomials are called the common factors of the terms of the polynomial. If the items of a polynomial have a common factor, you can propose this common factor to reduce the polynomial into the form of the product of two factors, and this method of factoring is called the common factor method.

2. Formula method.

If you reverse the multiplication formula, you can factor some polynomials, which is called the formula method.

Precautions. 1. The left side of the equation must be a polynomial;

2. The result of factoring must be expressed in the form of a product;

3. Each factor must be an integer, and the number of each factor must be lower than the number of the original polynomial;

4. Decompose the factors until each polynomial factor can no longer be decomposed.

Cross multiplication, undetermined coefficient method, double cross multiplication, symmetric polynomial, rotational symmetric polynomial method, coincidence theorem method, and there is no universally applicable method for finding the common factor decomposition. In the competition, there are also splitting and adding and subtracting terms, changing the element method, long division, short division, division, etc.

Note three principles:

1. The decomposition should be thorough (whether there is a common factor and whether a formula can be used).

2. The final result is only parentheses.

3. In the final result, the coefficient of the first term of the polynomial is positive (for example: -3x2+x=x(-3x+1)), but the first term is not necessarily positive, such as -2x-3xy-4xz=-x(2+3y+4z).

1）（a+b）³＝a³＋3a²b＋3ab²＋b³

2）a³+b³=a³+a²b-a²b+b³=a²（a+b）-b（a²-b²）=a²（a+b）-b（a+b）（a-b）

a+b）[a²-b（a-b）]=a+b）（a²-ab+b²）

3）a³-b³=a³-a²b+a²b-b³=a²（a-b）+b（a²-b²）=a²（a-b）+b（a+b）（a-b）

a-b）[a²+b（a+b）]=a-b）（a²+ab+b²）

I hope you have seen it useful and helpful to you.

Factorization is an important concept in mathematics that refers to splitting a polynomial into simpler forms of multiplication. Factorization is widely used in algebraic operations, function graphics, equation solving, etc. If you want to learn factoring well, you need to master the following steps:

First, it's important to understand the basic structure and terminology of polynomials, such as coefficients, powers, terms, and so on. Secondly, it is necessary to learn to use the common factor Gong Sakura old-fashioned potato stupidity, such as the square difference formula, the cubic difference formula, the binomial theorem, and so on.

The polynomial can then be factored into a simple form of product by means such as parentheses, collocation methods, or factorization formulas.

Finally, it is necessary to strengthen the practice and application of mathematics songs, do more related topics, and flexibly use techniques such as derivation, deformation, and factorization in the thinking process, so as to gradually improve the proficiency and accuracy of factorization.

In conclusion, factoring is a process that requires patience and enthusiasm, and as long as you study carefully and practice consistently, you will definitely be able to master this important mathematical skill.

Summary. Of course, in order to learn factorization well, of course, you must master the knowledge of integer multiplication and division before, because factorization and integer multiplication are opposite processes.

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Factorization is actually very simple, and I feel that it is difficult to learn the knowledge at first, and I feel that it is a new thing to contact a mess of scum! 1: Be good at asking (ask teachers, classmates, etc.) 2:

Be good at independent thinkingQuestion 3: Do more questions about factorization4: Read more tutorial textbooks about factorization That's all I know, I learned this way, I hope it will help you.

Of course, in order to learn factorization well, of course, you must master the knowledge of integer multiplication and division before, because factorization and integer multiplication are opposite processes.

It's very simple, do more questions, like some cross multiplication complete formula square difference, and the numbers are the same after learning.

1. Factor 2x -7x+3.

Analysis: First decompose the quadratic term coefficients and write them in the upper left and lower left corners of the cross line, then decompose the constant terms and write them in the upper right and lower right corners of the cross line, and then multiply them to find the algebraic sum so that it is equal to the primary term coefficient.

Decompose quadratic coefficients (take only positive factors):

Decomposition Constant Term:

The method of drawing crosses is used to represent the following four situations:

After observation, the fourth case is correct, and this is because after cross-multiplication, the algebraic sum of the two terms is exactly equal to the coefficient of the primary term 7

So it is equal to (x-3) (2x-1).

Second, let's have a simple factoring of x -5x+6.

The coefficient of the middle x is "-" and 6 is "+", which means that 6 is multiplied by two negative numbers, and these two negative numbers are homesick to -5

It is finally broken down into (x-2) (x-3).