show two polynomials interpolate the same data set I need some hint on this particular homework problem.

Show the following two polynomials $R(x)$ and $L(x)$ both interpolate the given points $$\left\{(x_1,\ y_1),\ (x_2,\ y_2),\ (x_3,\ y_3),\ (x_4,\ y_4)\right\}$$

I want to ask the community how I go about verifying they are interpolating the same data points? 
I am generalizing my question. I hope this is not too localized.
Is there some properties involved? My first thought was plugged in the points but $R(x)$ and $L(x)$ shouldn't give equal values... somehow I think I need to reconstruct the actual $f(x)$ function?
$$R(x) = 3 - 2(x+1) + 0 (x+1)(x) + (x+1)(x)(x-1)$$
$$L(x) = -1 +4(x+2) - 3(x+2)(x+1)+(x+2)(x+1)(x)$$
 A: The point of a polynomial interpolating a set of points is that they must intercept those points. An easy example would be two points and a line. What does it mean for the line to interpolate the two points? It would mean that the line passes through both of the points. In particular, if $f$ is your interpolating polynomial, then you must show that
$$f(x_i) = y_i$$
for each $(x_i,\ y_i)$. There is perhaps a short cut in checking for small polynomials. If you have a set of $n$ points, then you can always find a polynomial of degree at most $n-1$ which interpolates the set of points, moreover this polynomial is unique. If you have two polynomials of degree less than or equal to $n-1$, then at least one of the two cannot interpolate the set of points.
You have four points and two different degree three polynomials. Only one of these can actually interpolate the points.
Edit: Ah, I see the polynomials are actually the same. That explains a bit.
A: Expand the two polynomials and collect terms. They're both equal (to $x^3-3x+1$) so of course they'll both interpolate (or not) the set of points.
