Identify the degree, end behavior and roots ( with multiplicities) of the following polynomials. Factorization T1. Identify the degree, end behavior and roots (wit(a) f(x) = r³(x +1)²(x² + 9)(x² – 4)(b) /(x) = 4z (27-9)"(고 - 2) (x + 6)"%3D2. Use the following info

Answered: 1. Identify the degree, end behavior…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Identify the degree, end behavior and roots ( with multiplicities) of the following polynomials.

Factorization T
1. Identify the degree, end behavior and roots (wit
(a) f(x) = r³(x +1)²(x² + 9)(x² – 4)
(b) /(x) = 4z (27-9)"(고 - 2) (x + 6)"
%3D
2. Use the following info

Expert Solution

Step 1

Degree of polynomial is the highest power of 'x' on polynomial equation

Roots are found when f(x) = 0 gives real vales of x for which f(x) = 0.

End behavior of polynomial is the value of f(x) when x tend to +/- infinity.

$a) f (x) = x^{3} {(x + 1)}^{2} (x^{2} + 9) (x^{2} - 4) D e g r e e h i g h e s t d e g r e e i s f o u n d b y a d d i n g' x' p o w e r o f h i g h e s t o r d e r . f (x) = x^{3} (x^{2} + 2 x + 1) (x^{2} + 9) (x^{2} - 4)' x' h i g h e s t p o w e r = 3 + 2 + 2 + 2 = 9 = d e g r e e o f f (x) E n d b e h a v i o r p u t x \to \infty f (x) \to \infty p u t x \to - \infty f (x) \to - \infty R o o t s f (x) = 0 x^{3} = 0 \Rightarrow x = 0, 0, 0 or, x + 1 = 0 \Rightarrow x = - 1 or, x^{2} - 4 = 0 \Rightarrow x = + 2 or - 2 So, roots = 0, - 1, 2, - 2$