1, formula method: factorization is carried out by using basic formulas such as square difference formula, complete square formula and cubic difference formula. For example, for polynomial a? -B? We can decompose its factor into (a+b) (a-b) by the square difference formula.
2. Method of extracting common factors: Find common factors in polynomials and extract them, thus simplifying polynomials. For example, for the polynomial AX+BX, we can extract the common factor x(a+b) to get X (A+B).
3. cross multiplication: for some polynomials, we can decompose them into the product of two polynomials, each of which consists of a constant and the power of x, such as the polynomial ax? +bx+c, we can decompose it into the form of (px+q) (rx+s), where p, r, q and s are constants and pqrs = c.
The role of factorization
1, simplified expression: factorization can express a polynomial in a simpler form, making the mathematical expression more concise and clear. This is helpful to better understand and remember mathematical formulas. Factorization can make some seemingly complicated mathematical calculations simple and easy. For example, some polynomials that cannot be solved directly can be decomposed into the product of several polynomials, so that the solution of the original polynomial can be obtained by solving each polynomial.
2. Wide application: Factorization is widely used in many mathematical problems. For example, when solving some geometric problems, in order to better study their properties, it is necessary to decompose some complex geometric figures into some simple ones. In addition, factorization is also widely used in algebra, trigonometry, number theory and other fields.
3. Problem solving: Factorization is an important method to solve problems. For example, when solving some equations, we can factorize the equations and transform them into several simpler equations, which makes it easier to find the answers to the questions. Factorization also plays an important role in solving some geometric problems.