The polynomal is expressed as the equation of a plane and an orthogonal
basis set up using the unit normal, the unit vector pointing from the
intersection of the normal with the plane, to the intersection of the plane
with the coordinate axes. From there the space curve in x is projected onto
the basis. Tensor operations lead to more calculatable results. With this
range of freedom 3D slices of the nD situation precipitate roots to the
polynomial using the quadradic formula.
The illusion is the truth. Only the math lies.
Jon Giffen