Find a polynomial p_3p
3
​
such that \left\{p_{0}, p_{1}, p_{2}, p_{3}\right\}{p
0
​
,p
1
​
,p
2
​
,p
3
​
} is an orthogonal basis for the subspace \mathbb{P}_3P
3
​
of \mathbb{P}_4P
4
​
. Scale the polynomial p_3p
3
​
so that its vector of values is (1, 2, 0, -2, 1).