polyfit uses Vandermonde matrix to do the calculation, not least squares.
You require an 8th order polynomial and you have 9 input points. There are exact solutions for the fit (to within round-off) using techniques such as lagrange interpolating polynomial. Least squares is not one of those exact solution techniques, not unless you are using it in a degenerate sense.
I have to wonder, then, whether the question is expecting you to use curve fitting, or expecting you to construct a sum-of-squares residue function and minimize that function ?