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怎样分解因式xxxx–7xx–18用什么方法?我需要一个完...

x^4-7x²-18 =(x²-9)(x²+2) =(x-3)(x+3)(x²+2)

x^4+8x^3+15x^2-4x-20 =x^2(x^2+8x+15)-4(x+5) =x^2(x+5)(x+3)-4(x+5) =(x+5)[(x+3)x^2-4] =(x+5)(x^3+3x^2-4) =(x+5)(x^3+2x^2+x^2-4) =(x+5)[x^2(x+2)+(x+2)(x-2)] =(x+5)(x+2)(x^2+x-2) =(x+5)(x+2)(x-1)(x+2) =(x+5)(x-1)[(x+2)^2]

原式=x⁴+2x²+1++(x³+x)+(x³+x²+x) =(x²+1)²+x(x²+1)+(x³+x²+x) =(x²+1)(x²+1+x)+x(x²+x+1) =(x²+x+1)(x²+x+1) =(x²+x+1)²

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