§1 引言这一章的教材内容包括着:①在教学了二次三项式的因式分解的基础上,研究整函数的因式分解;②在数的概念的扩展的基础上,比较完整地讨论有理整函数的因式分解的意义;③在教学了一元一次方程、一元二次方程和可以化为二次方程的方程的基础上,进一步研究一元高次方程的根和它的解法,以及它的根与系数间的关系。因此它是存总结性的教材,也是为了今后学习高等代数奠定一个基础。在现行中学数学教学大纲和课本中没有提到求高次方程的无理根,高次方程的重根,以及倒数方程等问题。关于求高次方程的无理根的问题,虽然它是一个理论联系实际的题材,但是它牵涉的面较广,必须增添方程变形的定理和有关连续函数性质的定理,这些定理对中学生来说是比较不容易接受的,所以在目前情 § 1 Introduction The teaching materials of this chapter include: 1 On the basis of the factorization of the secondary trinomial, the factorization of the whole function is studied; 2 Based on the expansion of the concept of numbers, it is relatively complete. The significance of the factorization of rational whole functions is discussed. 3 On the basis of the teaching of a one-dimensional first-order equation, a one-dimensional quadratic equation, and an equation that can be converted into a quadratic equation, the root of the unitary higher-order equation and its solution are further studied. And its relationship between roots and coefficients. Therefore, it is a summarizing teaching material, and it also lays a foundation for studying advanced algebra in the future. In the current middle school mathematics syllabus and textbooks, there are no mentions of the irrational roots of high-order equations, the re-roots of high-order equations, and reciprocal equations. Regarding the question of the unreasonable root of higher order equations, although it is a subject that relates theory to practice, it involves a wide range of topics. The theorem of equation deformation and the theorems on the properties of continuous functions must be added. These theorems are for middle school students. It is not easy to accept, so in the present situation