Question

因式分解 1.（x+1)(X+3)(x+5）（X+7）+15 2.x三次方+x-2 3.x九次方+x六次方+x三次方-3拜托各位大神

要过程………………………………

Answer 1

1.（x+1)(X+3)(x+5）（X+7）+15 ={(x^2+8x)+7)}{x^2+8x)+15}+15, 设x^2+8x=t (t+7)(t+15)+15=t2+22t+120=(t+10)(t+12) 所以{(x^2+8x)+7)}{x^2+8x)+15}+15={(x^2+8x)+10)}{x^2+8x)+12}=(x^2+8x+10)(x+2)(x+6) 2.x三次方+x-2 x^3+x-2=x^3-1+x-1=(x-1)(x^2+x+2) 3.x九次方+x六次方+x三次方-3 x^9+x^6+x^3-3=(x^3)^3+(x^3)^2+x^3-3,设x^3=t t^3+t^2+t-3=(t-1)(t^2+t+1)+(t-1)(t+1)+(t-1)=(t-1)(t^2+2t+3) 所以x^9+x^6+x^3-3=(x^3)^3+(x^3)^2+x^3-3=(x^3-1)(x^6+2x^3+3) =(x-1)(x^2+x+1)(x^6+2x^3+3)

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