a)
w(x)=x^3-2x^2-x+2=x^2(x-2)-(x-2)=(x-2)(x^2-1)=(x-2)(x-1)(x+1)
b)
w(x)=x^3+3x^2-4x-12=x^2(x+3)-4(x+3)=(x+3)(x^2-4)=(x+3)(x-2)(x+2)
c)
w(x)=3x^3-x^2+6x-2=x^2(3x-1)+2(3x-1)=(3x-1)(x^2+2)
d)
w(x)=3x^4-15x^3-6x^2+30x=3x(x^3-5x^2-2x+10)=
3x[x^2(x-5)-2(x-5)]=3x(x-5)(x^2-2)=3x(x-5)(x-\sqrt2)(x+\sqrt2)
e)
w(x)=2x^4-8x^3+3x^2-12x=x(2x^3-8x^2+3x-12)=x[2x^2(x-4)+3(x-4)]=x(x-4)(2x^2+3)
f)
w(x)=x^5-x^3-x^2+1=x^3(x^2-1)-(x^2-1)=(x^2-1)(x^3-1)=(x-1)(x+1)*(x-1)(x^2+x+1)=(x-1)^2(x+1)(x^2+x+1)