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 bothx and x^2 we have to solve the system of equations

= 0

= 0

Which gives us

p=

So if we want p to be orthogonal to both

Which gives us

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