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?
$R(x) = 3 - 2(x+1) + 0 (x+1)(x) + (x+1)(x)(x-1)$ $L(x) = -1 +4(x+2) - 3(x+2)(x+1)+(x+2)(x+1)(x)$