因式分解 x四次方+3x三次方-6x-4

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因式分解 x四次方+3x三次方-6x-4
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因式分解 x四次方+3x三次方-6x-4
因式分解 x四次方+3x三次方-6x-4

因式分解 x四次方+3x三次方-6x-4
x四次方+3x三次方-6x-4
=(x^4-4)+3x(x^2-2)
=(x^2-2)(x^2+2)+3x(x^2-2)
=(x^2-2)(x^2+2+3x)
=(x+1)(x+2)(x^2-2)
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x四次方+3x三次方-6x-4
=x^4+x³+2x³+2x²-2(x²+3x+2)
=x³(x+1)+2x²(x+1)-2(x+1)(x+2)
=(x+1)(x³+2x²-2x-4)
=(x+1)[x²(x+2)-2(x+2)]
=(x+1)(x+2)(x²-2)
=(x+1)(x+2)(x+√2)(x-√2)

(X平方-2)(X+1)(X+2)