Interpolation: The pointsXy-2-1124 -1 3-459 4 24 -53lie on a polynomial. Use (for example) the divided difference table of Newton's method to determinethe degree of the polynomial.

Given data is as given the following table. x y -2 -1 1 2 4 59 -1 4 3 24 -4 -53…

Answered: Interpolation: The points X y -2 -1 1 4…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

SectionP.3: Polynomials And Special Products

Problem 91E

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Similar questions

Using Descartes’ Rule of Signs. we can tell that the polynomial P(x)=x53x4+x2+8x8 has _______________, ____________________positive real zeros and _____________negative real zeros.
DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same. P(x)=3x45x3+x23x+5 Q(x)=(((3x5)x+1)x3)x+5 Try to evaluate P(2) and Q(2) in your head, using the forms given. Which is easier? Now write the polynomial R(x)=x52x4+3x32x2+3x+4 in nested form, like the polynomial Q. Use the nested form to find R(3) in your head. Do you see how calculating with the nested form follows the same arithmetic steps as calculating the value of a polynomial using synthetic division?
In Exercises 2-6, fill in the blanks. A shortcut for long division of polynomials is ,in which the divisor must be of the form xk.
DISCUSS: Degrees of Sums and Products of Polynomials Make up several pairs of polynomials, then calculate the sum and product of each pair. On the basis of your experiments and observations, answer the following questions. (a) How is the degree of the product related to the degrees of the original polynomials? (b)How is the degree of the sum related to the degrees of the original polynomials? (c) Test your conclusions by finding the sum and product of the following polynomials: 2x3+x3 and 2x3x+7

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Interpolation: The points X y -2 -1 1 4 -1 3-4 2 59 4 24 -53 lie on a polynomial. Use (for example) the divided difference table of Newton's method to determine the degree of the polynomial.