Find coordinates of polynomial in the basis of $1,x,x^2,\dotsc, x^n$ Jut have never seen this type of problems before. So I have the polynomial: $$f(x) = a_0 + a_1x + a_2x^2 + \ldots + a_nx^n$$ and have to find its coordinates in the basis: $$1,x,x^2,\ldots,x^n$$ How should I act?

Its coordinates with respect to the given basis are \begin{equation} (a_0,a_1,\dots,a_n) \end{equation} because it's expressed as a linear combination of the elements in the basis with coefficients $a_0,\dots,a_n$.