当m为何值时x^2-y^2-2x+6y+m可分解为两个一次因式

显示全部楼层 · 2008-12-13 00:35:34

如题，谢谢
分解因式x^4+3x^3+2x^2+3x+1
因式分解x^2-2ax-b^2+2ab

千问 · 2008-12-13 00:35:34

x^2-y^2-2x+6y+m=(x+y)(x-y)-2x+6y+m=(x+y+a)(x-y+b)=(x+y)(x-y)+a(x-y)+b(x+y)+ab=(x+y)(x-y)+(a+b)x+(b-a)y+ab所以a+b=-2b-a=6ab=m所以a=-4,b=2m=ab=-8x^4+3x^3+2x^2+3x+1=(x^4+2x^2+1)+(3x^3+3x)=(x^2+1)^2+3x(x^2+1)=(x^2+1)(x^2+3x+1)x^2-2ax-b^2+2ab=(x^2-b^2)-2ax+2ab=(x+b)(x-b)-2a(x-b)=(x-b)(x+b-2a)...