一些因式分解的題目...能解的就盡量吧!

Question

１‧x^5-2x^4+3x^3-6x^2-4x+8
２‧x^2-y^2+2yz-z^2
３‧x^2-5x-6
４‧(xy+1)(x+1)(y+1)+xy
５‧4x^2+y^2-z^2-4xy

Answer 1

１‧x^5-2x^4+3x^3-6x^2-4x+8
x^4(x-2)+3x^2(x-2)-4(x-2)
＝(x-2)(x^4+3x^2-4)
＝(x-2)(x^4)(x+1)(x-1)

２‧x^2-y^2+2yz-z^2
x^2-(y^2-2yz+z^2)
＝x^2-(y-z)^2
＝(x+y-z)(x-y+z)

３‧x^2-5x-6
(x-6)(x+1)

４‧(xy+1)(x+1)(y+1)+xy
(xy+1)(xy+x+y+1)+xy
＝(xy+1)^2(x+y)(xy+1)+xy
＝(xy+x+1)(xy+y+1)

５‧4x^2+y^2-z^2-4xy
(2x-y)^2-z^2
＝(2x-y-z)(2x-y+z)

2006-02-14 22:11:20 補充：
有的我以前有做過.有的有做過類似的...所以回答起來也比較輕鬆~^^

2006-02-14 22:12:30 補充：
忘了打一個"+"４‧(xy+1)(x+1)(y+1)+xy(xy+1)(xy+x+y+1)+xy＝(xy+1)^2+(x+y)(xy+1)+xy＝(xy+x+1)(xy+y+1)

2006-02-15 17:08:25 補充：
１‧x^5-2x^4+3x^3-6x^2-4x+8
x^4(x-2)+3x^2(x-2)-4(x-2)
＝(x-2)(x^4+3x^2-4)
＝(x-2)(x^2+4)(x+1)(x-1)

打錯了>"<

Answer 2

３‧x^2-5x-6　＝　(x-6)(x+1)