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一、引言多項式的因式分解,往往是根据不同情况采取不同的分解方法。在中学里所使用的一些方法,基本上是提取公因式法、利用乘法公式法和分組分解法等,很少有一般的分解方法。对中学生要求到这样程度也就可以了。但对中学教师来說,口掌握特殊方法还是不够的,应尽可能掌握一些一般的分解方法。一个变数的有理数系数任意次多項式的因式分解,在个別的高等代数里已經提到它在有理数体上的一般分解方法。这个方法是此較麻煩的,但它有一个好处,能分解或不能分解通过它我們都能知道,而且能分解时能把它分解出来。我这里所写的实系数多变数二次多項式的因式分解問題是来研究实系数多变数的二次多項式在实数体上的一般分解方法。作起来虽然也比較麻煩,但能分解或不能分解它都能給以肯定的解答。这篇文章是我个人的点滴体会,可能有缺点和錯誤,請讀者給以指正。
I. INTRODUCTION The factorization of polynomials is often based on different conditions to take different decomposition methods. Some of the methods used in secondary schools are basically the extraction of common factor methods, the use of multiplication formulas, and group decomposition methods. There are few general decomposition methods. It is all right to ask the middle school students to such a degree. However, for secondary school teachers, the mastery of special methods is not enough, and as far as possible, some general decomposition methods should be mastered. The factorization of polynomials of an arbitrary number polynomial of a rational number coefficient of a variable has already been mentioned in some higher algebras as a general decomposition method for rational numbers. This method is more troublesome, but it has an advantage. It can be decomposed or cannot be decomposed through it. We can all know it, and it can be decomposed when it can be decomposed. The factorization problem of the multivariable quadratic polynomial of real coefficients I wrote here is a general decomposition method of the quadratic polynomials on real numbers to study the multivariables of real coefficients. Although it is more troublesome to perform, it can give a positive answer if it can be decomposed or cannot be decomposed. This article is my personal experience, there may be shortcomings and errors, ask the reader to correct me.