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x^3+3x%4如何分解为(x%1)(x^2+x+4)?

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

(x-1)(x+2)(x+3)(x+4)+24 应该是这个吧: (x+1)(x+2)(x+3)(x+4)-24 =(x+1)(x+4)(x+2)(x+3)-24 =(x²+5x+4)(x²+5x+6)-24 =(x²+5x)²+10(x²+5x)+24-24 =(x²+5x)(x²+5x+10) =x(x+5)(x ²+5x+10)

x^3=4-3x x^3+3x-4=0 x^3-x^2+x^2+3x-4=0 x^2(x-1)+(x+4)(x-1)=0 (x-1)(x^2+x+4)=0

直接开方法就是一步一步算 移项 合并同类项 望采纳 谢谢

4(3X^2-X-1)(X^2+2x-3)-(4x^2+x-4)? =4(3X^2-X-1)(X^2+2x-3)-(4x^2+x-4)^2 =4(3X^2-X-1)(X^2+2x-3)-[(3x^2-x-1)+(x^2+2x-3)]^2 =-[(3x^2-x-1)-(x^2+2x-3)]^2 =-(2x^2-3x+2)^2

可以用长除法,也就是多项式除法,用f(x)去除以x-1. 也可以用配凑法: f(x)=4x³-4x²-8x²+8x+12x-12 =4x²(x-1)-8x(x-1)+12(x-1) =(x-1)(4x²-8x+12) =4(x-1)(x²-2x+3)

供参考。

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

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