1.2x^3+x^2-13X+6
=(2x^3-4x^2)+(5x^2-10x)+(-3x+6)
=2x^2(x-2)+5x(x-2)-3(x-2)
=(x-2)(2x^2+5x-3)
=(x-2)(x+3)(2x-1).
2.x^4+x^2+1
=(x^4+2x^2+1)-x^2
=(x^2+1)^2-x^2
=(x^2+x+1)(x^2-x+1).
3.ab(a+b)^2-(a+b)^2+1
=ab(a+b)^2-a(a+b)-b(a+b)+1
=a(a+b)[b(a+b)-1]-[b(a+b)-1]
=(b^2+ab-1)(a^2+ab-1).
4.x^4+2001x^2+2000x+2001
=(x^4-x)+(2001x^2+2001x+2001)
=x(x-1)(x^2+x+1)+2001(x^2+x+1)
=(x^2+x+1)(x^2-x+2001).
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