Question

高中的因式分解~~急就帮忙

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

Answer 1

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)

Answer 2

2x^2－5xy－12y^2＋8x＋y＋6
=(x-4y)(2x+3y)+8x＋y＋6

=(x-4y+3)(2x+3y+2)

x^2＋2x－12
=（x-2）（x^2+2x+6）

x的5次方－x^2－28
=(x-2)(x^4+2x^3+4x^2+7x+14)

x^3+y^3+z^3-3xyz
= (x^3+3yx^2+3xy^2+y^3)+z^3-3xyz-3yx^2-3xy^2
= (x+y)^3+z^3-3xy(x+y+z)
= (x+y+z)[(x+y)^2-(x+y)z+z^2]-3xy(x+y+z)
= (x+y+z)[(x^2+2xy+y^2-xz-yz+z^2)-2xy]
= (x+y+z)(x^2+y^2+z^2-xy-yz-zx)