Why is it necessary to compose n-1 equations when obtaining a polynomial (of degree n)?

Question

Mathematics

I get a polynomial through the least squares method (I smooth out statistical data), in this method it is necessary to compose a SLAE in order to find the coefficients at X (more details here ), it is logical to assume that the number of unknowns, for example, with a polynomial of 5 degrees of 6 pieces (a + bx + cx ^ 2 ... ) therefore, it is necessary to compose 6 equations to find 6 unknowns, however, the primary source clearly states that the number of equations must be composed by n-1 i.e. 4 why so?

Answer 1

I looked through the information on your link, it says about the k + 1 (0,...,k) equation for approximating the polynomial of the kth degree. N is the number of observations.