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

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

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.5: Solution Of Cubic And Quartic Equations By Formulas (optional)

Problem 30E

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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) = −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

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