How to guess the divisible integer by long division Long division is also called big division. For example: x ^ 3 + 3x-4, how do you know that he can divide by X-1 to get the remaining factor? I mainly want to know how to guess that he has X-1 ? Why divide by X-1 instead of other factors, such as x-3, X-2, etc. How do you know it's divided by X-1?

How to guess the divisible integer by long division Long division is also called big division. For example: x ^ 3 + 3x-4, how do you know that he can divide by X-1 to get the remaining factor? I mainly want to know how to guess that he has X-1 ? Why divide by X-1 instead of other factors, such as x-3, X-2, etc. How do you know it's divided by X-1?

The more obvious point is the principle of "merging similar terms". Pay attention to the times and coefficients of each term, and add one term and then subtract this term. Finally, you can get the remaining X-1, which can be divided completely. The main problem is to use (x ^ 3-3x ^ 2 + 3x-1) = (x-1) ^ 3