數學因式分解二題~~!!

Question

因式分解下列各式:(1)x^4+x^3+6x^2+5x+5 (2)x^4-x^3-7x^2+13x-6

主要是第二題~~誰可以敎敎我~!

Answer 1

(1)   (x2+x+1)(x2+5)      x4 +x3 +6x2 +5x +5  = x4 +x3 +  x2 +5x2 +5x +5  = x4 +x3 +  x2 +5x2 +5x +5  = x4 +x3 +  x2 +5x2 +5x +5  = x2(x2 +x +1) + 5(x2 +x +1)  = x2(x2 +x +1) + 5(x2 +x +1)  = x2(x2 +x +1) + 5(x2 +x +1)  = (x2 +x +1)(x2 +5) (2)   (x-1)2(x+3)(x-2)      x4 -x3 -7x2 +13x -6 = (x4 -x3) + ( -7x2 +13x -6 ) = x3(x-1) + (-7x+6)(x-1) = ( x-1 )( x3 -7x +6 ) = ( x-1 )( x-1 )( x2+x-6) = ( x-1 )2( x2+x-6 ) = ( x-1 )2 ( x+3 )( x-2 )這題不難....觀察後面的 -7x2 +13x -6 可以發現他就是(-7x+6)(x-1)                                     (用十字交乘可知)..接著算下去就會有柳暗花明又一村的感覺了.....

2005-08-15 22:23:58 補充：
系統怪怪的...SHOW回答有點LAG....

Answer 2

我解第二題
題目 = ( x^4-x^3-2x^2) - (5x^2-13x+6)
= x^2(x^2-x-2) - (x-2)(5x-3)
= x^2(x-2)(x+1) - (x-2)(5x-3)
= (x-2) (x^3+x^2-5x+3)
= (x-2) (x^3-x^2 + 2x^2 - 2x - 3x + 3 )
=(x-2) [x^2(x-1) +2x (x-1) -3 (x-1)]
= (x-2) (x-1) (x^2 + 2x -3)
= (x-2) (x-1) (x+3) (x-1)
= (x-1)^2 (x-2) (x+3)