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On the interval $[-3,3]$ we know that $x$ and $x^2$ are orthogonal. Let $p=x+ax^2+bx^3$ . Then

$\langle p,x \rangle =$

$\langle p,x^2 \rangle =$

So if we want p to be orthogonal to both $x$ and $x^2$ we have to solve the system of equations

$= 0$

$= 0$

Which gives us
$p=$

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