Question: a. Show that the cubic polynomials P(x) = 3 2(x + 1) + 0(x + 1)(x) + (x + 1)(x)(x 1) And Q(x)

a. Show that the cubic polynomials
P(x) = 3 ˆ’ 2(x + 1) + 0(x + 1)(x) + (x + 1)(x)(x ˆ’ 1)
And
Q(x) = ˆ’1 + 4(x + 2) ˆ’ 3(x + 2)(x + 1) + (x + 2)(x + 1)(x)
Both interpolate the data

b. Why does part (a) not violate the uniqueness property of interpolating polynomials?

f(x) 33

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