A polynomial $ p(x)$ is such that $p(0) =5, p(1) = 4, p(2) = 9 $ and $p(3) = 20 $.
What is the minimum degree it can have?
The problem can easily be solved by hit and trial method. First assuming that the degree is 1, then 2 and so on until the initial conditions are satisfied. This method gives the answer as 2, for the above problem.
But in spite of checking each and every value, starting from 1; is there any better approach to solve such problems ?
Many thanks !!