论文部分内容阅读
在初中代数“整式乘除”一章中,经常遇到求具有某种整除性质代数式的字母系数问题.学生可以使用的工具只有两个:1.竖式除法;2.整除的定义与性质.有代表性的例子如下:例1 已知代数式x~4+ax~3+7x~2-13x+10含有因式x+5,求字母a的值.例2 已知x~2-3x+2整除2x~4-ax~3 -X~2+bX-4,求字母a、b的值.处理上述问题的常规方法(如课本中)是:用竖式除法求出余式,由整除的定义知余式为零,可求出字母系数的值.如本例,余式=(b-7a+27)x+(6a-30),由b-7a+27=0,6a-30=0,解出a=5,b=8.这种方法虽然有效,但无法避免繁琐的代数式竖式除法.特别当字母是代数式中较高次项的系数时,将越除越繁,计算量也随之越来越大.对于基础不太扎实、计算能力较差的学生,经常会出现各种各样的错误.
In the chapter of “multiplication, division and division of algebra” in junior high school algebra, we often encounter the problem of finding the algebraic algebraic letter coefficient. There are only two tools that students can use: 1. vertical division; 2. the definition and nature of divisibility. Representative examples are as follows: Example 1 The algebraic expressions x~4+ax~3+7x~2-13x+10 contain the factor x+5 and find the value of the letter a. Example 2 Known x~2-3x+2 Divide 2x~4-ax~3 -X~2+bX-4 and find the values of the letters a and b. The conventional method for dealing with the above problem (as in textbooks) is: use the vertical division to find the remainder, divisible by By defining the remainder formula as zero, the value of the letter coefficient can be calculated. As in this example, the remainder formula is (b-7a+27)x+(6a-30), and b-7a+27=0,6a-30=0. , Solve for a=5, b=8. Although this method is effective, but can not avoid the cumbersome algebraic vertical division. Especially when the letter is the coefficient of higher order terms in algebraic formula, the more the more complex, the amount of calculation also As the students become less solid and have poor computing skills, they often have a variety of mistakes.