Choose the best answer for each question:

1 Of the following polynomial interpolation methods, which is generally considered the method of choice due to its relative ease of use?

2 Which method is the best choice when the desired degree of the interpolating polynomial is known?

3 Which method is best suited when the desired degree of the interpolating polynomial is unknown?

4 Which method is best suited to the addition of points to the data set?

5 What is the computational cost of finding an interpolating polynomial through $n$ points using the Newton form?

6 What is the computational cost of the Vandermonde method, using Gaussian elimination?

7 Under what conditions can the Lagrange method of polynomial interpolation fail?

8 Given a set of $n$ points, exactly how many interpolating polynomials can be found to pass through the points?

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