$a)$

$\{\begin{array}{l}w\left(0\right)=5\\ w\left(1\right)=-3\end{array}$

$\{\begin{array}{l}-2\cdot 0^3+3\cdot 0^2+a\cdot 0+b=5\\ -2\cdot 1^3+3\cdot 1^2+a\cdot 1+b=-3\end{array}$

$\{\begin{array}{l}b=5\\ -2+3+a+b=-3\end{array}$

$\{\begin{array}{l}b=5\\ a=-3-1-b=-4-5=-9\end{array}$

$b)$