$\text{a)}w\left(x\right)=2x^6+12x^4+18x^2=2x^2\left(x^4+6x^2+9\right)=2x^2{\left(x^2+3\right)}^2$

$\text{b)}w\left(x\right)=-2x^5+20x^3-50x=-2x\left(x^4-10x^2+25\right)=-2x{\left(x^2-5\right)}^2=-2x{\left[\left(x-\sqrt{5}\right)\left(x+\sqrt{5}\right)\right]}^2=-2x{\left(x-\sqrt{5}\right)}^2{\left(x+\sqrt{5}\right)}^2$