Answer
The numbers are not of absolute precision, rounded by octave: $$p(t)=1.71250t-1.19479t^2+0.66146t^3-0.07005t^4+0.00260t^5$$
Work Step by Step
Write down the augmented matrix and the reduce it with your software.
if you try to use a polynomial of degree less than 5, the reduced echelon form indicates the system is not consistent.
