(a) Given the data $f(0)=0, f(1)=4, f(2)=2, f(3)=8$, find the interpolating cubic polynomial $p_{3} \in \mathbb{P}_{3}[x]$ in the Newton form.

(b) We add to the data one more value, $f(-2)=10$. Find the interpolating quartic polynomial $p_{4} \in \mathbb{P}_{4}[x]$ for the extended data in the Newton form.