$a)$

$S=x^3-x+2x^4-2=2x^4+x^3-x-1$

$T=4-x^3+3x^2+x^4=x^4-x^3+3x^2+4$

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

$=\underline{2x^4}+\underline{\underline{x^3}}-x-\underline{\underline{\underline{1}}}+\underline{x^4}-\underline{\underline{x^3}}+3x^2+\underline{\underline{\underline{4}}}=$

$=3x^4+3x^2-x+3$