   Chapter 3.3, Problem 73E Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
ISBN: 9781305071759

Solutions

Chapter
Section Precalculus: Mathematics for Calcu...

7th Edition
James Stewart + 2 others
ISBN: 9781305071759
Textbook Problem

Finding a Polynomial from a Graph Find the polynomial of the specified degree whose graph is shown.73. Degree 4 To determine

The 4 degree polynomial from the given graph.

Explanation

Factor theorem states that the value of a given polynomial P(x) is zero at (x=c) if (xc) is a factor of P(x) . And its converse is also true, it states that (xc) is a factor of the polynomial P(x) , if and only if P(x)=0 at (x=c) .

The graphical representation of the square function, that is f(x)=[A(x)]2 , at point (x=0) is given as,

Figure 1

And the graphical representation of a polynomial is,

Figure 2

From the graph, the given polynomial P(x) is zero (or meets the xaxis ) at two different point as (2 and 1)

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