 Solution

ID: past-exam-of-the-options-i-course-of-the-university-of-oxford/2006/p/p1/i/solution

p (x) = x^{2} - 2 x

already has degree at most three and gives the specified data at every node. Uniqueness of polynomial interpolation therefore gives

p (x) = x^{2} - 2 x .

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