x^4-4x+3因式分解

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x^4-4x+3因式分解

x^4-4x+3因式分解
x^4-4x+3因式分解

x^4-4x+3因式分解
原式
=x⁴-1-4x+4
=(x²+1)(x+1)(x-1)-4(x-1)
=(x-1)(x³+x²+x+1-4)
=(x-1)[(x³-1)+(x²-1)+(x-1)]
=(x-1)²(x²+x+1+x+1+1)
=(x-1)²(x²+2x+3)

(x-1)(x-1)(x^2+2x+3)
原式=x^4-x^2+x^2-4x+3=(x-1)(x^3+x^2+x-3)=
(x-1)(x-1)(x^2+2x+3)