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