 Solution

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

Let

f (x) = x^{4} - 6 x^{3} + 11 x^{2} - 5 x

. The node polynomial is

ω (x) = x (x - 1) (x - 2) (x - 3) = x^{4} - 6 x^{3} + 11 x^{2} - 6 x .

It vanishes at all four nodes, so subtracting it leaves the data unchanged. Since

f (x) - ω (x) = x

p (x) = x .

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