若f(x)除以(x-1)(x-2)(x-3)余式为2x^2+x-7则f(x)除以x-1余式为多少,f(x)除以(x-2)(x-3)余式为多少
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 15:10:35
![若f(x)除以(x-1)(x-2)(x-3)余式为2x^2+x-7则f(x)除以x-1余式为多少,f(x)除以(x-2)(x-3)余式为多少](/uploads/image/z/12480166-46-6.jpg?t=%E8%8B%A5f%EF%BC%88x%EF%BC%89%E9%99%A4%E4%BB%A5%EF%BC%88x-1%EF%BC%89%EF%BC%88x-2%EF%BC%89%EF%BC%88x-3%EF%BC%89%E4%BD%99%E5%BC%8F%E4%B8%BA2x%5E2%2Bx-7%E5%88%99f%EF%BC%88x%EF%BC%89%E9%99%A4%E4%BB%A5x-1%E4%BD%99%E5%BC%8F%E4%B8%BA%E5%A4%9A%E5%B0%91%2Cf%EF%BC%88x%EF%BC%89%E9%99%A4%E4%BB%A5%EF%BC%88x-2%EF%BC%89%EF%BC%88x-3%29%E4%BD%99%E5%BC%8F%E4%B8%BA%E5%A4%9A%E5%B0%91)
若f(x)除以(x-1)(x-2)(x-3)余式为2x^2+x-7则f(x)除以x-1余式为多少,f(x)除以(x-2)(x-3)余式为多少
若f(x)除以(x-1)(x-2)(x-3)余式为2x^2+x-7则f(x)除以x-1余式为多少,
f(x)除以(x-2)(x-3)余式为多少
若f(x)除以(x-1)(x-2)(x-3)余式为2x^2+x-7则f(x)除以x-1余式为多少,f(x)除以(x-2)(x-3)余式为多少
若f(x)除以(x-1)(x-2)(x-3)余式为2x²+x-7
因为2x²+x-7除以x-1余式为-4
所以f(x)除以x-1余式为-4
因为2x²+x-7除以(x-2)(x-3)余式为11x-19
所以f(x)除以(x-2)(x-3)余式为11x-19
因为f(x)除以(x-1)(x-2)(x-3)的余式为2x^2+x-7,
那么可以设f(x)=g(x)(x-1)(x-2)(x-3) +2x^2+x-7,
显然f(x)除以(x-1)时,g(x)(x-1)(x-2)(x-3)除以(x-1)不会有余式,
故只求2x^2+x-7除以(x-1)的余式即可,
而2x^2+x-7=(x-1)(2x+3) -4,
即2x...
全部展开
因为f(x)除以(x-1)(x-2)(x-3)的余式为2x^2+x-7,
那么可以设f(x)=g(x)(x-1)(x-2)(x-3) +2x^2+x-7,
显然f(x)除以(x-1)时,g(x)(x-1)(x-2)(x-3)除以(x-1)不会有余式,
故只求2x^2+x-7除以(x-1)的余式即可,
而2x^2+x-7=(x-1)(2x+3) -4,
即2x^2+x-7除以(x-1)的余式为 -4,
所以f(x)除以(x-1)的余式就是 -4
收起
由题意,设:
f(x)=(x-1)(x-2)(x-3)A+(2x²+x-7)
=(x-1)(x-2)(x-3)A+(x-1)(2x+3)-4
=(x-1)[(x-2)(x-3)A+(2x+3)]-4
所以:f(x)除以(x-1)余数是-4。