Find a polynomial $p$ of degree $3$ if its value in $4$ points is given Find a polynomial $p$ of degree $3$ such that
\begin{align*}
p(−4) &= −142, \\
p(1) &= −2, \\
p(−5) &= −242, \\
p(4) &= 10.
\end{align*}
Then use your polynomial to approximate $p(2)$.
\begin{align*}
p(x) &= ?, \\
p(2) &= ?.
\end{align*}
I can't find this sort of question in the textbook so I'm having trouble.
Please teach me how to solve this question and, perhaps, fill in point 2?
Thank you.

Hint: Find constants $a$, $b$, $c$ and $d$ such that the polynomial
$$a(x-1)(x+5)(x-4)+b(x+4)(x+5)(x-4)+c(x+4)(x-1)(x-4)+d(x+4)(x-1)(x-5)$$
takes on the desired values. 
For example, to compute $a$, we want $a(-4-1)(-4+5)(-4-4)=-142$. 
