1)x²+x-(a²-a)
=x²+x-a²+a
=(x²-a²)+(x+a)
=(x+a)(x-a)+(x+a)
=(x+a)(x-a+1)
2) x5+x4+x3+x2+x+1
= (x5+x4)+(x³+x²)+(x+1)
=x4(x+1)+x²(x+1)+(x+1)
=(x+1)(x4+x²+1)
=(x+1)[(x4+2x²+1)-x²]
=(x+1)[(x²+1)²-x²]
=(x+1)(x²+x+1)(x²-x+1)
3)3x2+5xy-2y2+x+9y-4
因为 3x²+5xy-2y²=(3x-y)(x+2y)
所以设 3x²+5xy-2y²+x+9y-4=(3x-y+a)(x+2y+b)
左边=3x²+5xy-2y²+(a+3b)x+(2a-b)y+ab
所以 a+3b=1,2a-b=9,ab=-4
解得 a=4,b=-1
所以 3x²+5xy-2y²+x+9y-4=(3x-y+4)(x+2y-1)
4）x2(x+1)-y(xy+x)
=x³+x²-y²x-xy
=x(x²+x-y²-y)
=x[(x²-y²)+(x-y)]
=x[(x+y)(x-y)+(x-y)]
=x(x-y)(x+y+1)
5.x2(x-1)2+32(x-x2)+60
=x²(x-1)²-32x(x-1)+60
=[x(x-1)]²-32[x(x-1)]+60 【把x（x-1）看做一项】
=(x²-x-30)(x²-x-2)
=(x-6)(x+5)(x-2)(x+1)
6）.2(x2+6x+1)2+5(x2+1)(x2+6x+1)+2(x2+1)2
设 x²+6x+1=a,x²+1=b
原式=2a²+5ab+2b²
=(2a+b)(a+2b)
=(2x²+12x+2+x²+1)( x²+6x+1+2x²+2)
=(3x²+12x+3)(3x²+6x+3)
=9(x²+4x+1)(x²+2x+1)
=9(x²+4x+1)(x+1)²
7）(x+1)(x+3)(x+5)(x+7)+15
=[(x+1)(x+7)][(x+3)(x+5)]+15
=(x²+8x+7)(x²+8x+15)+15
设 x²+8x+11=a
原式=(a-4)(a+4)+15
=a²-1
=(a+1)(a-1)
= (x²+8x+12)( x²+8x+10)
=(x+2)(x+6) (x²+8x+10)
8.已知1+w+w2=0,求w1980+w1981+------+w2009的值
w1980+w1981+------+w2009
=w1980(1+w+w2)+w1083(1+w+w2)+……+w2007(1+w+w2)
=0+0+……+0
=0