a)

$w\left(x\right)=5\sqrt{5}{x}^5+x^2=x^2\left(5\sqrt{5}{x}^3+1\right)=x^2\left({\left(\sqrt{5}x\right)}^3+1^3\right)\stackrel{a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)}{=}{x}^2\left(\sqrt{5}x+1\right)\stackrel{\Delta =5-20<0}{\left(5x^2-\sqrt{5}x+1\right)}$

b)

$w\left(x\right)=x^6-0,125x^3=x^3\left(x^3-0,125\right)=x^3\left(x^3-{\left(0,5\right)}^3\right)\stackrel{a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)}{=}{x}^3\left(x-0,5\right)\stackrel{\Delta =0.25-1<0}{\left(x^2+0.5x+0.25\right)}$