“ax~2+bx+c”是关于x的二次三项式,在证(解)题时,我们往往失去隐含的“ax~2+bx+c”而导致思路闭塞,或方法呆板,如果能把握住“ax~2+bx+c”及其常用的结构特征,在解题中将会显示出它的奇功妙效,使复杂的问题得到简捷明快地解决,兹将它在解题中的应用分类陈述如下: 一因式分解多项式的因式分解,一般常用分组分解法,有些问题若将特征式整理为关于某一字母的二次三项式,就转化为我们所熟悉的问题了。例1 分解因式:ab(a-b)+bc(b-c)+ca(c-a)。解:将原式整理为关于a的二次三项式,即 “ax~2+bx+c” is about the quadratic trinomial of x. In the proof (solution) problem, we often lose the implicit “ax~2+bx+c” and result in mental blockage, or the method is dull. If we can grasp the “ax~2+bx+c” and its common structural features, we will show its miraculous effect in the problem solving, so that the complex issues can be solved simply and clearly, and we will The application classification in the problem-solving problem is stated as follows: 1. The factorization of factorization polynomials is commonly used in the group decomposition method. Some problems are converted into familiar ones if they are organized into the quadric terms of a certain letter. The problem is. Example 1 Decomposition factor: ab(a-b)+bc(b-c)+ca(c-a). Solution: Organize the original formula into a quadratic trinomial about a, ie