Final answer:
To satisfy 9 boundary conditions, we would expect a polynomial of at least degree 8, as the minimum degree is one less than the number of specified boundary conditions.
Step-by-step explanation:
If we specify 9 boundary conditions, then we would expect a polynomial of at least degree 8. The general rule for determining the minimum degree of a polynomial, based on the number of boundary conditions, is that the number of boundary conditions is equal to the degree of the polynomial plus one. Hence, to satisfy 9 boundary conditions, we should look for a polynomial that is one degree less, since the constant term (degree 0) also counts as a condition.
For example, if you have a polynomial f(x) = ax^8 + bx^7+ cx^6 + dx^5 + ex^4 + gx^3 + hx^2 + ix + j, it has 9 coefficients (a to j) that can be varied to meet the 9 boundary conditions. The polynomial's highest power term would be x^8, making it an 8th-degree polynomial.