Try q(x)=(x2+1)3 with n=6. The space of polynomials p(x) such that ∫10p(x)q(x)dx∈Qπ is infinite-dimensional. If you meant polynomials of degree <6, that has dimension 4, as the
following 4 linearly independent polynomials p(x) qualify:
4x−3,x2,4x3−1,x4+1
Robert Israel
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