Factorization method (1) common factor method.
(1) common factor: the common factor of each term is called ~ of this polynomial term.
② Extraction method of common factor: Generally speaking, white, if every term of a polynomial has a common factor, you can put this common factor outside brackets and write the polynomial in the form of factor product. This factorization method is called extracting common factors.
am+bm+cm=m(a+b+c)
③ Specific methods: When all the coefficients are integers, the coefficients of the common factor formula should take the greatest common divisor of all the coefficients; The letter takes the same letter for each item, and the index of each letter takes the lowest degree. If the first term of a polynomial is negative, a "-"sign is usually put forward to make the coefficient of the first term in brackets positive.
⑵ Use the formula method.
① variance formula:. a 2-b 2 = (a+b) (a-b)
② Complete square formula: a 2 2ab+b 2 = (a b) 2.
Polynomials that can be decomposed by the complete square formula must be trinomials, two of which can be written as the sum of squares of two numbers (or formulas), and the other is twice the product of these two numbers (or formulas). ※ 。
③ Cubic sum formula: A 3+B 3 = (A+B) (A 2-AB+B 2).
Cubic difference formula: a 3-b 3 = (a-b) (a 2+ab+b 2).
④ Complete cubic formula: a 3 3a 2b+3ab 2 b 3 = (a b) 3.
⑤a^n-b^n=(a-b)a^(n- 1)+a^(n-2)b+……+b^(n-2)a+b^(n- 1)
A m+b m = (a+b) a (m-1)-a (m-2) b+...-b (m-2) a+b (m-1) (m is an odd number).
⑶ Grouping decomposition method
Grouping decomposition: a method of grouping polynomials and then decomposing factors.
The grouping decomposition method must have a clear purpose, that is, the common factor can be directly extracted or the formula can be used after grouping.
(4) Methods of splitting and supplementing projects
Decomposition and supplement method: one term of polynomial is decomposed or filled with two terms (or several terms) which are opposite to each other, so that the original formula is applicable to common factor method, formula method or group decomposition method; It should be noted that the deformation must be carried out under the principle of equality with the original polynomial.
5] Cross multiplication.
① factorization of x2+(pq) x+pq formula
The characteristics of this kind of quadratic trinomial formula are: the coefficient of quadratic term is1; Constant term is the product of two numbers; The coefficient of a linear term is the sum of two factors of a constant term. So we can directly decompose some quadratic trinomial factors with the coefficient of1:x 2+(pq) x+pq = (x+p) (x+q).
② Factorization of KX2+MX+N formula
If it can be decomposed into k = AC, n = BD and AD+BC = M, then
kx^2+mx+n=(axb)(cxd)
Introduction to Factorization Factorization is one of the most important identical deformations in middle school mathematics. It is widely used in elementary mathematics, seeking roots and solving quadratic equations with one variable in mathematics. It is a powerful tool to solve many mathematical problems.
Factorization is flexible and ingenious. Learning these methods and skills is not only necessary to master the content of factorization, but also plays a very unique role in cultivating problem-solving skills and developing thinking ability. Learning it can not only review the four operations of algebraic expressions, but also lay a good foundation for learning scores; Learning it well can not only cultivate students' ability of observation, thinking development and calculation, but also improve students' ability of comprehensive analysis and problem solving.
The above is some information about factorization, I hope it will help you.