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factorize(x^2-x)^2-4(x^2-x)-12

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factorize(x^2-x)^2-4(x^2-x)-12 煩請寫出詳盡STEP~ THX~

最佳解答:

1. Factorize (x^2-x)^2-4(x^2-x)-12 Answer: Let y be (x^2-x). Rewrite the formula, y^2-4y-12 = (y^2-6y) + (2y-12) = y(y-6) + 2 (y-6) = (y+2) (y-6) Because y= x^2-x Therefore, (y+2) (y-6) = (x^2-x+2) (x^2-x-6) = (x^2-x+2) (x^2-3x + 2x-6) = (x^2-x+2) (x(x-3) + 2(x-3)) = (x^2-x+2) (x+2) (x-3) -----------------------------------------------------------------------------------------

其他解答:

(x^2-x)^2-4(x^2-x)-12 =2x^4-x^2-4x2+4x-12 =2x^4-5x^2+4x-1----------------------It is the answer. 2008-08-15 21:57:42 補充： The answer is 2x^4-5x^2+4x-12 Sorry|||||(x2-x)2-4(x2-x)-12 =[(x2-x)-6][(x2-x)+2] =(x2-x-6)(x2-x+2) 2008-08-16 12:52:25 補充： 漏左一步: =(x^2-x-6)(x^2-x+2) =(x-3)(x+2)(x^2-x+2)