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读了本刊今年第一期《十字相乘法的一种灵活应用》一文,颇受启发,仔细思索,发现该文的方法还可以多样,运用范围也可以扩大,特提出两点补充意见如下。一对形如x~3+Bx~2+Cx+D的三次四项式,有时拆C要比拆B简单些。这是因为三次项的系数是1,它只能分成1×1,而D则可能分解成多种不同的整数的乘积,会给拆项增加困难。例如,易知x~3+8x~2+17x+10=x(x+2)(x+6)+5(x+2),x~3+16x~2+11x+6=x(x+2)(x+3)+3(x+2),一般地。拆C之后,原式成为x(x
After reading the article “A Flexible Application of Cross-Multiply Method” in the first issue of this year’s edition of the journal, he was inspired and thought carefully. He found that the method of this article can also be varied and the scope of application can be expanded. Specially, the following two points are added as follows: . A pair of cubic quadruplicates such as x~3+Bx~2+Cx+D are sometimes simpler to remove C than B. This is because the coefficient of the cubic term is 1, it can only be divided into 1 × 1, and D may be decomposed into a product of many different integers, which will increase the difficulty of splitting. For example, it is easy to know x~3+8x~2+17x+10=x(x+2)(x+6)+5(x+2), x~3+16x~2+11x+6=x(x +2)(x+3)+3(x+2), generally. After removing C, the original formula becomes x (x