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整系数多项式的整数根,通常用综合除法、余数定理和整数根定理来寻求。整数根定理是: 一个整系数多项式的整数根必须是该多项式常数项的一个因子。这是整数根之的必要条件,但不是充分的。在一些情形下,“可能零点”的个数很多,例如:f(x)=x~5-17x~4+20x~3-65x~2+19x-48根据整数根定理,f(x)的整数根“只”可能是±1、±2、±3、±4、±6、±8、±12、±16、±24、±48,一看到这么一长串数字就足以使学生感到沮丧和厌烦。但是我们可以通过一些简单的心算,对这个表作大刀阔斧
Integral roots of polynomials of integral coefficients are usually sought using synthetic division, remainder theorem, and integer root theorem. The integer root theorem is: The integer root of an integer coefficient polynomial must be a factor of the polynomial constant term. This is a necessary condition for the integer root, but it is not sufficient. In some cases, the number of “possible zeros” is many, for example: f(x)=x~5-17x~4+20x~3-65x~2+19x-48 according to the root theorem of integer, f(x) The integer root “only” may be ± 1, ± 2, ± 3, ± 4, ± 6, ± 8, ± 12, ± 16, ± 24, ± 48. Depressed and tired. But we can use this simple mental calculation to make a bold decision on this table.