Let P
3
have the inner product given by evaluation at −5,−1,1, and 5 . Let p
0
(t)=4,p
1
(t)=2t, and q(t)=
12
t
2
−13
. Notice that these polynomials form an orthogonal set with this inner product. Find the best approximation to p(t)=3t
3
by polynomials in Span {p
0
,p
1
,q}. The best approximation to p(t)=3t
3
by polynomials in Span{p
0
,p
1
,q} is .