①原式=(x²+x+1)²-(x²+x+1)-6=(x²+x+3)(x²+x-2)=(x²+x+3)(x+2)(x-1)
②原式=(x²+2x)²+(x²+2x)-20=(x²+2x+5)(x²+2x-4)=(x²+2x+5)(x+1+根号5)(x+1-根号5)
③原式=(x+1)(x+2)(x-4)(x-5)
④原式=(a²+5a+6)(a²+7a+6)+a²=(a²+6a+6-a)(a²+6a+6+a)+a²=(a²+6a+6)²
⑤原式=(x²+8x+7)(x²+8x+15)-9=(x²+8x+11)²-25
=(x²+8x+16)(x²+8x+6)=(x+4)²(x+4+根号10)(x+4-根号10)
⑥原式=[(a+b)-(c+d)]²+4(a+b)(c+d)=(a+b)²+(c+d)²+2(a+b)(c+d)=(a+b+c+d)²
⑦原式=2x²+(y+2)x-(2y-1)(3y-4)=(2x-3y+4)(x+2y-1)
⑧原式=x²+(2y-4)x-(2y+3)(4y-1)=(x+4y-1)(x-2y-3)
⑨A=(a-2b)²+(b+1)²+99 当a=2b,b=-1时 A 取得最小值99
10.(a-1/2)²+(b+2)²=0,得 a=1/2 b=-2 a²+b²=17/4
11.原式=(x²+3x+1)²-2(x²+3x+1)-8=(x²+3x+3)(x²+3x-3)