多项式x^4+2x^3-4x^2-2x+3与x^3+4x^2+x-6的最大公因式是什么x^4+2x^3-4x^2-2x+3=(x^4+3x^3)-x(x^2+4x+3)+(x+3)=x^3(x+3)-x(x+1)(x+3)+(x+3)=(x+3)[x^3-x(x+1)+1]=(x+3)[x^3+1-x(x+1)]=(x+3)[(x+1)(
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 03:36:46
![多项式x^4+2x^3-4x^2-2x+3与x^3+4x^2+x-6的最大公因式是什么x^4+2x^3-4x^2-2x+3=(x^4+3x^3)-x(x^2+4x+3)+(x+3)=x^3(x+3)-x(x+1)(x+3)+(x+3)=(x+3)[x^3-x(x+1)+1]=(x+3)[x^3+1-x(x+1)]=(x+3)[(x+1)(](/uploads/image/z/1349150-14-0.jpg?t=%E5%A4%9A%E9%A1%B9%E5%BC%8Fx%5E4%2B2x%5E3-4x%5E2-2x%2B3%E4%B8%8Ex%5E3%2B4x%5E2%2Bx-6%E7%9A%84%E6%9C%80%E5%A4%A7%E5%85%AC%E5%9B%A0%E5%BC%8F%E6%98%AF%E4%BB%80%E4%B9%88x%5E4%2B2x%5E3-4x%5E2-2x%2B3%EF%BC%9D%28x%5E4%EF%BC%8B3x%5E3%29%EF%BC%8Dx%28x%5E2%EF%BC%8B4x%EF%BC%8B3%29%EF%BC%8B%28x%EF%BC%8B3%29%EF%BC%9Dx%5E3%28x%EF%BC%8B3%29%EF%BC%8Dx%28x%EF%BC%8B1%29%28x%EF%BC%8B3%29%EF%BC%8B%28x%EF%BC%8B3%29%EF%BC%9D%28x%EF%BC%8B3%29%5Bx%5E3%EF%BC%8Dx%28x%EF%BC%8B1%29%EF%BC%8B1%5D%EF%BC%9D%28x%EF%BC%8B3%29%5Bx%5E3%EF%BC%8B1%EF%BC%8Dx%28x%EF%BC%8B1%29%5D%EF%BC%9D%28x%EF%BC%8B3%29%5B%28x%EF%BC%8B1%29%28)
多项式x^4+2x^3-4x^2-2x+3与x^3+4x^2+x-6的最大公因式是什么x^4+2x^3-4x^2-2x+3=(x^4+3x^3)-x(x^2+4x+3)+(x+3)=x^3(x+3)-x(x+1)(x+3)+(x+3)=(x+3)[x^3-x(x+1)+1]=(x+3)[x^3+1-x(x+1)]=(x+3)[(x+1)(
多项式x^4+2x^3-4x^2-2x+3与x^3+4x^2+x-6的最大公因式是什么
x^4+2x^3-4x^2-2x+3
=(x^4+3x^3)-x(x^2+4x+3)+(x+3)
=x^3(x+3)-x(x+1)(x+3)+(x+3)
=(x+3)[x^3-x(x+1)+1]
=(x+3)[x^3+1-x(x+1)]
=(x+3)[(x+1)(x^2-x+1)-x(x+1)]
=(x+3)(x+1)(x^2-2x+1)
=(x+3)(x+1)(x-1)(x-1)
=(x+3)(x-1)(x+1)(x-1)
x^3+4x^2+x-6
=(x^3+3x^2)+(x^2+x-6)
=x^2(x+3)+(x-2)(x+3)
=(x+3)(x^2+x-2)
=(x+3)(x-1)(x+2)
所以多项式x^4+2x^3-4x^2-2x+3与x^3+4x^2+x-6的最大公因式是(x+3)(x-1)
看到有人这么做,可是我想不出这么提怎么办
辗转相除法能做吗?
多项式x^4+2x^3-4x^2-2x+3与x^3+4x^2+x-6的最大公因式是什么x^4+2x^3-4x^2-2x+3=(x^4+3x^3)-x(x^2+4x+3)+(x+3)=x^3(x+3)-x(x+1)(x+3)+(x+3)=(x+3)[x^3-x(x+1)+1]=(x+3)[x^3+1-x(x+1)]=(x+3)[(x+1)(