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 students' problem-solving skills and developing their thinking ability.
Definition: transforming a polynomial into the product of several simplest algebraic expressions is called factorization of this polynomial (also called factorization).
Significance: It is one of the most important identical deformations in middle school mathematics. It is widely used in elementary mathematics and is a powerful tool for us to solve many mathematical problems. The factorization method is flexible and skillful. Learning these methods and skills is not only necessary to master the content of factorization.
But also plays a very unique role in cultivating students' problem-solving skills and developing their 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' observation, thinking development and calculation ability, but also improve students' comprehensive analysis and problem-solving ability.
Factorization factor and algebraic expression multiplication are reciprocal.
At the same time, it is also an important step to solve the quadratic equation in one variable by factorization.
Extended data
The common factor of each term is called the common factor of each term of this polynomial. The common factor can be a monomial or a polynomial.
If every term of a polynomial has a common factor, it can be put forward, so that the polynomial can be transformed into the product of two factors. This method of decomposing factors is called. Be sure to extract the common factor and decomposition factor.
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 of each item, and the index of each letter takes the smallest number.
When the coefficient of each term has a score, the common factor coefficient is the greatest common divisor of each score. 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 become positive. When the "-"sign is put forward, the terms of the polynomial should be changed.
Formula: find the right common factor and extract it all at once; The whole family moved out and left 1 to look after the house; The negative sign should be changed, and the deformation depends on parity.
References:
Baidu factorization encyclopedia