A polynomial is transformed into the product of several algebraic expressions in a value domain (real value domain decomposition, that is, all terms are real numbers). The deformation of this formula is called factorization of this polynomial, which is also called factorization of this polynomial. Factorization is one of the most important identical deformations in middle school mathematics, and it is widely used in elementary mathematics.
It is also widely used in mathematics to find roots and solve quadratic equations with one variable, and 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. Basic conclusion: Factorization is the inverse process of algebraic expression multiplication.
Advanced conclusion: In advanced algebra, factorization has some important conclusions, which are difficult to prove at the level of elementary algebra, but easy to understand. Factorization is closely related to solving higher-order equations. Linear equation and quadratic equation have relatively fixed and easy-to-master methods in junior high school. There are also fixed formulas for solving cubic equations and quartic equations.
principle
1. The factorization factor is an identical deformation of a polynomial, and the left side of the equation must be a polynomial.
2. The result of factorization must be expressed in the form of product.
3. Each factor must be an algebraic expression, and the degree of each factor must be lower than that of the original polynomial.
4. In the end, only brackets are left, and factorization must be carried out until each polynomial factorization can no longer be decomposed; The first term of the polynomial of the result is generally positive. Extract the common factor from a formula, that is, recombine through the formula, and then extract the common factor.