$a)w\left(x\right)=-3x^4-3x^2-3$

$b){\left(-1\right)}^4={\left(-1\right)}^2={\left(-1\right)}^0=1\Rightarrow a_0=a_2=a_4=1$

${\left(-1\right)}^3={\left(-1\right)}^1=-1\Rightarrow a_3=a_1=-1$

$w\left(x\right)=x^4-x^3+x^2-x+1$