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)(

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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)(
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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)(