1, the multiplication of each term should be clearly remembered: before extracting the common factor, the coefficient of each term and the letter of each term need to be clear. Only by understanding these can we correctly extract the common factor.
2. The laws of symbols should be distinguished: when extracting common factors, we need to pay attention to the changing laws of symbols. For example, if the first term of a polynomial is negative, the sign of the whole polynomial will change after the common factor is extracted. Therefore, it is necessary to carefully analyze the symbolic laws of each item to avoid mistakes.
3, the coefficient is the same as before: when extracting the common factor, we should simplify the coefficient of each item as much as possible to 1. This process can be realized by mathematical methods such as shifting terms and subtracting points. At the same time, if there are the same factors between projects, they need to be extracted at the same time.
4. Factorization is the purpose: the ultimate purpose of extracting common factors is to decompose polynomials into simpler factorial forms. This process can be achieved by constantly breaking down polynomials into smaller parts. For example, for a trinomial, we can first split it into two binomials, then extract the common factors respectively, and finally get a simpler factorial form.
Application of extracting common factors;
1. Score: The extracted common factor can be used for score reduction. Dividing the numerator and denominator by the same factor can make the fraction into a simpler form, which is convenient for comparison and calculation.
2. Simplify expressions: extracting common factors can be used to simplify complex mathematical expressions. By extracting the same factor from multiple terms, the whole expression can be more concise and convenient for mathematical operation and understanding.
3. Solving equations: extracting common factors can be used to solve some equations. For example, when solving a quadratic equation with one variable, the left side of the equation can be transformed into the product of two linear factors by extracting the common factor, so as to get the solution of the equation.
4. Factorization: Extracting common factors is a common method of factorization. By extracting common factors from polynomials, polynomials can be decomposed into simpler factor forms, which is convenient for further analysis and understanding.
5. Mathematical induction: In mathematical induction, extracting common factors can simplify the summation formula. By extracting the same factor from multiple terms, the summation formula can be more concise and easy to remember and apply.