1、x^3-9x+8=(x-1)(x^2-x+8)
2、x^9+x^6+x^3-3=(x^9-1)+(x^6-1)+(x^3-1)
=(x^3-1)(x^6+x^3+1+x^3+1+1)
=(x^3-1)(x^6+2x^3+3)
3、(m^2-1)(n^2-1)+4mn=m^2n^2-m^2-n^2+1+4mn
=(mn)^2+2mn+1-(m^2+n^2-2mn)
=(mn+1)^2-(m-n)^2
=(mn+m-n+1)(mn-m+n+1)
4、a^3*b-ab^3+a^2+b^2+1
=(ab+b^2+1)(a^2-ab+1)
二、换元法：
5、6x^4+7x^3-36x^2-7x+6
＝x^2(6(x^2+1/x^2)+7(x-1/x)-36)
=x^2(6(x-1/x)^2+7(x-1/x)-24)
=x^2(2x-2/x-3)(3x-3/x+8)
=(2x^2-3x-2)(3x^2+8x-3)
=(2x+1)(x-2)(3x+1)(x-3)
6、(x^2+3x+2)(4x^2+8x+3)-90
＝（x+1）(x+2)(2x+1)(2x+3)-90
=(2x^2+5x+2)(2x^2+5x+3)-90 (将2x^2+5x+2看作整体)
=(2x^2+5x+2)^2+(2x^2+5x+2)-90
=(2x^2+5x+2-9)(2x^2+5x+2+10)
=(x-1)(2x+7)(2x^2+5x+12)
7、(x^2+xy+y^2)-4xy(x^2+y^2)暂时不会做.