Polynomial Interpolation

With an interpolation, we are only interested in the properties of the function at the specified interpolation points, so there is no need to worry about the form of the functions elsewhere or to sketch them (although feel free to explore this if you are interested!).

Don't be tempted to expand out Steve's expression, as this will hide the properties of the construction which allow you to see generalisations.

To get started, try substituting in a point and see what cancels or vanishes!