How to do factoring to explain 200

There is no universal method of factorization, and the common factor method and formula method are mainly introduced in junior high school mathematics textbooks. In the competition, there are split terms and addition and subtraction methods, group decomposition method and cross multiplication, pending coefficient method, double cross multiplication, symmetric polynomial, rotational symmetric polynomial method, coincidence theorem method, root finding formula method, commutation method, long division, short division, division, etc. (Actually, the classic example question:

1.Decompose factor(1+y) 2-2x 2(1+y 2)+x 4(1-y) 2 solution: original formula = (1+y) 2+2(1+y)x 2(1+y)+x 4(1-y) 2-2(1+y)x 2(1-y)-2x 2(1+y 2) =[(1+y)+x 2(1-y)] 2-2(1+y)x 2(1-y)-2x 2(1+y 2) =[(1+y)+x 2(1-y)] 2-(2x) 2 =[(1+y)+x 2(1- y)+2x]· [1+y)+x 2(1-y)-2x] =(x 2-x 2y+2x+y+1)(x 2-x 2y-2x+y+1) =[(x+1) 2-y(x 2-1)][x-1) 2-y(x 2-1)] =(x+1)(x+1-xy+y)(x-1)(x-1-xy-y) 2.

Proof that for any number x,y, the value of the following formula will not be 33 x 5+3x 4y-5x 3y 2+4xy 4+12y 5 Solution: original = (x 5+3x 4y)-(5x 3y 2+15x 2y 3)+(4xy 4+12y 5) =x 4(x+3y)-5x 2y 2(x+3y)+4y 4(x+3y) =(x+3y)(x 4-5x 2y 2+4y 4) =(x+3y)(x 2-4y 2)(x 2-y 2) =(x+3y)(x+y)(x-y)(x+2y)(x-2y) is to complicate a simple problem) Note the three principles 1 Decomposition should be thorough 2 The final result is only parentheses 3 The coefficient of the first term of the polynomial in the final result is positive (e.g.

3x 2+x=x(-3x+1)) Inductive method: 1. Mention the common factor method in the textbook of the Shanghai Science and Technology Edition. 2. Formula method.

3. Group decomposition method. 4. Make-up method. [x 2 + (a + b) x + ab = (x + a) (x + b)] 5. Combinatorial decomposition method.

6. Cross multiplication. 7. Double cross multiplication. 8. Matching method.

9. Split the method. 10. Substitution method. 11. Long division.

12. Addition and subtraction. 13. Root-seeking method. 14. Image method.

15. Principal Method. 16. Pending coefficient method. 17. Special value method.

18. Factoring theorem.

The coefficient of the quadratic term and the constant term are multiplied and then multiplied. Then add it up to see if the number is a one-time term.

For example: x*x-3x-4=0

The constant term -4 (be sure to pay attention to the symbol) can be split into -4 and +1 (multiplication is -4) -4*1+1*1 (1 is the coefficient of the quadratic term that is split) = -3 (the number of the primary term), so the factor is decomposed into (x-4) (x+1) = 0

x -4x +1

This is also a way to write a list, and the equation is written horizontally. Multiply, it's diagonal.

For example: 2x*x-x-15=0

2x +5x -3

Split the quadratic term into 2x and x, and multiply it by 2x*xThe constant term is split into +5 and -3, and the multiplication is the number of the coefficient of the primary term of the original equation) This one is like **, and the answer is to look sideways, and the answer is (2x+5)(x-3)=0, and the calculation coefficient is to look at the diagonal multiplication.

I don't know if you get it. If you don't understand, you can ask me again.

The coefficient method to be determined, the coefficient can be found, and the general one can be found and simplified.

eg:(ax+b)(cx+d)simplify,The coefficients of the formula are equal,You can specify a,b,c,d as any number,(except 0),Then find the other three numbers,And then simplify.。。。

Factorization is only realized by yourself, if you rely on others to tell you, there are too many methods, only by doing special training questions can you experience, have your own experience, and there are methods to do any problems.

Principles:1The result is left with only parentheses.

2.The first term of the polynomial for the result is positive. The common factor is extracted within a formula, that is, the common factor is reorganized through the formula, and then the common factor is extracted.

3.The first coefficient in parentheses cannot be negative;

4.If there is a multiplication of a monomial and a polynomial, the mononomial should be placed before the polynomial. e.g. a(a+b).

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, whether there is a formula), 2 The final result is only parentheses.

3 In the final result, the coefficient of the first term of the polynomial is positive (e.g., -3x2+x=x(-3x+1)), which does not necessarily mean that the first term is positive, e.g., -2x-3xy-4xz=-x(2+3y+4z).

This question should be y (m+1)-y (m-1), right?

Then it is easy to see that there is a common factor y (m-1) in y (m+1)-y (m-1), so to extract the common factor y (m-1), we get y (m+1)-y (m-1)=y (m-1)*[y (2)-1]=y (m-1)(y-1)(y+1).

First, look at the coefficients of the terms, and if they are not cogeneous, then the greatest common factor of the coefficients should be part of the common factor;

Then, see if each item has the same alphabetic or polynomial factor, and if so, bring it up until there is no common factor for each item;

Then see whether the whole formula is in the form of a certain formula, such as square difference, perfect square, cubic sum (difference), etc., if so, then decompose according to the formula method;

In the case of quadratic trinominals, cross multiplication can also be considered;

If none of the above works, you may want to sort out the equation first and then analyze it.

Note that when the number of formulas is high, it is usually necessary to have a holistic view.