a)
w(x)=x^4+2x^3-8x-16=x^3(x+2)-8(x+2)=(x+2)(x^3-8)=(x+2)(x-2)(x^2+2x+4)
b)
w(x)=14x^3-7x^2+4x-2=7x^2(2x-1)+2(x-1)=(x-1)(7x^2+2) …7x^2\ne-2
c)
w(x)=2x^3-6x^2+5x-15=2x^2(x-3)+5(x-3)=(x-3)(2x^2+5) … 2x^2\ne -5
d)
w(x)=x^4-3x^3+x-3=x^3(x-3)+(x-3)=(x-3)(x^3-1)=(x-3)(x-1)(x^2+x+1)
e)
w(x)=\frac{1}{2}x^3-\frac{1}{6}x^2-3x+1=\frac{1}{6}x^2(3x-1)-(3x-1)=(3x-1)(\frac{1}{6}x^2-1)=
=\frac{1}{6}(x^2-6)(3x-1)=\frac{1}{6}(3x-1)(x-\sqrt6)(x+\sqrt6)
f)
w(x)=\frac{2}{3}x^3-3x^2-6x+27=\frac{1}{3}x^2(2x-9)-3(2x-9)=(2x-9)(\frac{1}{3}x^2-3)=
\frac{1}{3}(x^2-9)(2x-9)=\frac{1}{3}(x-3)(x+3)(2x-9)
g)
w(x)=x^3-\sqrt2x^2+\sqrt2x-2=x^2(x-\sqrt2)+\sqrt2(x-\sqrt2)=(x-\sqrt2)(x^2+\sqrt2) …x^2\ne -\sqrt2
h)
w(x)=x^5+x^4-2x^3-2x^2+x+1=x^4(x+1)-2x^2(x+1)+(x+1)=(x+1)(x^4-2x^2+1)=
=(x+1)(x^2-1)^2=(x+1)[(x-1)(x+1)]^2=(x+1)^3(x-1)^2