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Chapter 4: Q. 41 (page 194)

In Problems 41鈥� 48, form a polynomial function whose real zeros and degree are given. Answers will vary depending on the choice of a leading coefficient.

Zeros:-1,1,3; Degree 3

Short Answer

Expert verified

The polynomial function isfx=x3-3x3-x+3

Step by step solution

01

Step 1. Given Information

The zeros of the polynomial are-1,1,3and degree is 3

02

Step 2. Forming a Polynomial Function

rIf is a real zero of a polynomial function f,then x-ris a factor of f.. This

means thatx--1,x-1,x-3are factors of f.. As a result, any polynomial function of the formfx=ax+1x-1x-3

03

Step 3. Solving the polynomial function

fx=x+1x-1x-3fx=x2-1x-3f(x)=x3-3x2-x+3

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Most popular questions from this chapter

x3+2x2-3x>0

The concentration C of a certain drug in a patient's bloodstream t hours after injection is given by

Ct=50tt2+25

Part (a): Find the horizontal asymptote of Ct. What happens to the concentration of the drug as t increases?

Part (b): Using your graphing utility, graph C=Ct.

Part (c): Determine the time at which the concentration is highest.

True or False. The graph of a rational function may intersect

a horizontal asymptote.

Find the real zeros of f. Use the real zeros to factor f.

f(x)=4x4-15x3-8x2+15x+4

Use the Factor Theorem to prove that x-c is a factor of

xn-cn for any positive integer n.
See all solutions

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