①2x²－5xy－12y²＋8x＋y＋6

题目

①2x²－5xy－12y²＋8x＋y＋6
②x³＋2x－12
③x的5次方－x²－28
④x³＋y³＋z³－3xyz

答案

1、(2x+3y)(x-4y)+8x+y+6
=(2x+3y+2)(x-4y+3)
2、x³-2x²+2x²-4x+6x-12
=x²(x-2)+2x(x-2)+6(x-2)
=(x-2)(x²+2x+6)
3、x的5次方-2x的4次方+2x的4次方-4x³+4x³-8x²+7x²-14x+14x-18
=x的4次方(x-2)+2x³(x-2)+4x²(x-2)+7x(x-2)+14(x-2)
=(x-2)(x的4次方+2x³+4x²+7x+14)
4、
x³+y³+z³-3xyz
= (x³+3yx²+3xy²+y³)+z³-3xyz-3yx²-3xy²
= (x+y)³+z³-3xy(x+y+z)
= (x+y+z)[(x+y)²-(x+y)z+z²]-3xy(x+y+z)
= (x+y+z)[(x²+2xy+y²-xz-yz+z²)-2xy]
= (x+y+z)(x²+y²+z²-xy-yz-zx)