(a) Given the data

\begin{tabular}{c|r|r|r|r} $x_{i}$ & $-1$ & 0 & 1 & 3 \ \hline$f\left(x_{i}\right)$ & $-7$ & $-3$ & $-3$ & 9 \end{tabular}

find the interpolating cubic polynomial $p \in \mathcal{P}_{3}$ in the Newton form, and transform it to the power form.

(b) We add to the data one more value $f\left(x_{i}\right)$ at $x_{i}=2$. Find the power form of the interpolating quartic polynomial $q \in \mathcal{P}_{4}$ to the extended data

\begin{tabular}{c|c|r|r|r|r} $x_{i}$ & $-1$ & 0 & 1 & 2 & 3 \ \hline$f\left(x_{i}\right)$ & $-7$ & $-3$ & $-3$ & $-7$ & 9 \end{tabular}$.$