a. Show that the cubic polynomials P(x) = 3 2(x + 1) + 0(x + 1)(x) + (x + 1)(x)(x 1) and

Chapter 3, Problem 3.2.11

(choose chapter or problem)

a. Show that the cubic polynomials P(x) = 3 2(x + 1) + 0(x + 1)(x) + (x + 1)(x)(x 1) and Q(x) = 1 + 4(x + 2) 3(x + 2)(x + 1) + (x + 2)(x + 1)(x) both interpolate the data x 2 1 0 1 2 f (x) 1 3 1 1 3 b. Why does part (a) not violate the uniqueness property of interpolating polynomials?

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