Numerical Analysis - Method of Undetermined Co-efficients

Having a lot of trouble with this one, not even sure where to start:

Q3: Use the method of undetermined coefficients to prove that, for two given points (different) and any gives values and there exists a unique polynomial p(x) of degree 3 such that:

[25 marks]

My lecturer has not specified whether or not MATLAB may be used. Is this question possible without it? If so, how do I go about it?

P.S - This **is** the correct forum for this, isn't it?