a. Answer Yes it is a factor. Explanation Calculation: Here, we will substitute 3 in the equation we get, x 4 − 4 x 3 − 7 x 2 + 22 x + 24 = 3 4 − 4 ( 3 ) 3 − 7 ( 3 ) 2 + 22 ( 3 ) + 24 = 0 Hence, the remainder is zero, thus ( x + 2 ) is a factor of the polynomial f ( x ) = x 4 − 4 x 3 − 7 x 2 + 22 x + 24 . b. To determine Find the remaining factors of f ( x ) . Answer ( x + 1 ) , ( x − 4 ) Explanation Calculation: Here, from above we will rewrite the polynomial x 4 − 4 x 3 − 7 x 2 + 22 x + 24 as: x 4 − 4 x 3 − 7 x 2 + 22 x + 24 = x 2 − 3 x − 4 = x 2 − 4 x + x − 4 = x ( x − 4 ) + 1 ( x − 4 ) = ( x + 1 ) ( x − 4 ) Hence, the remaining factors are ( x + 1 ) , ( x − 4 ) . c. To determine Write the complete factorization of f ( x ) . Answer f ( x ) = ( x − 4 ) ( x + 1 ) ( x + 2 ) ( x + 3 ) Explanation Calculation: Hence, the complete factorization of a function f is: f ( x ) = ( x − 4 ) ( x + 1 ) ( x + 2 ) ( x + 3 ) . d. To determine List all real zeros of f . Answer 4 , 3 , − 1 , − 2 Explanation Calculation: Here, we can see directly from the factors that all the real zeroes are 4 , 3 , − 1 , − 2 . Hence, the zeroes of the function f are 4 , 3 , − 1 , − 2 . e. To determine Graph the function by using graphing utility. Answer Explanation Calculation: Here, the graph of the function f ( x ) = x 4 − 4 x 3 − 7 x 2 + 22 x + 24 is: Hence, the results are shown in the graph.

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 2, Problem 28RE

To determine

Verify the given factor(s) of f(x) .

Expert Solution

Answer to Problem 28RE

Yes it is a factor.

Explanation of Solution

Calculation:

Here, we will substitute 3 in the equation we get,

x4−4x3−7x2+22x+24=34−4(3)3−7(3)2+22(3)+24=0

Hence, the remainder is zero, thus (x+2) is a factor of the polynomial f(x)=x4−4x3−7x2+22x+24 .

To determine

Find the remaining factors of f(x) .

Expert Solution

Answer to Problem 28RE

(x+1),(x−4)

Explanation of Solution

Calculation:

Here, from above we will rewrite the polynomial x4−4x3−7x2+22x+24 as:

x4−4x3−7x2+22x+24=x2−3x−4

=x2−4x+x−4

=x(x−4)+1(x−4)

=(x+1)(x−4)

Hence, the remaining factors are (x+1),(x−4) .

To determine

Write the complete factorization of f(x) .

Expert Solution

Answer to Problem 28RE

f(x)=(x−4)(x+1)(x+2)(x+3)

Explanation of Solution

Calculation:

Hence, the complete factorization of a function f is:

f(x)=(x−4)(x+1)(x+2)(x+3) .

To determine

List all real zeros of f .

Expert Solution

Answer to Problem 28RE

4,3,−1,−2

Explanation of Solution

Calculation:

Here, we can see directly from the factors that all the real zeroes are 4,3,−1,−2 .

Hence, the zeroes of the function f are 4,3,−1,−2 .

To determine

Graph the function by using graphing utility.

Expert Solution

Answer to Problem 28RE

EBK PRECALCULUS W/LIMITS, Chapter 2, Problem 28RE , additional homework tip 1

Explanation of Solution

Calculation:

Here, the graph of the function f(x)=x4−4x3−7x2+22x+24 is:

EBK PRECALCULUS W/LIMITS, Chapter 2, Problem 28RE , additional homework tip 2

Hence, the results are shown in the graph.

Chapter 2, Problem 27RE

Chapter 2, Problem 29RE

Chapter 2 Solutions

EBK PRECALCULUS W/LIMITS

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Prob. 64E Ch. 2.6 - Prob. 65E Ch. 2.6 - Prob. 66E Ch. 2.6 - Prob. 67E Ch. 2.6 - Prob. 68E Ch. 2.6 - Prob. 69E Ch. 2.6 - Prob. 70E Ch. 2.6 - Prob. 71E Ch. 2.6 - Prob. 72E Ch. 2.6 - Prob. 73E Ch. 2.6 - Prob. 74E Ch. 2.6 - Prob. 75E Ch. 2.6 - Prob. 76E Ch. 2.6 - Prob. 77E Ch. 2.6 - Prob. 78E Ch. 2.6 - Prob. 79E Ch. 2.6 - Prob. 80E Ch. 2.6 - Prob. 81E Ch. 2.6 - Prob. 82E Ch. 2.7 - Prob. 1E Ch. 2.7 - Prob. 2E Ch. 2.7 - Prob. 3E Ch. 2.7 - Prob. 4E Ch. 2.7 - Prob. 5E Ch. 2.7 - Prob. 6E Ch. 2.7 - Prob. 7E Ch. 2.7 - Prob. 8E Ch. 2.7 - Prob. 9E Ch. 2.7 - Prob. 10E Ch. 2.7 - Prob. 11E Ch. 2.7 - Prob. 12E Ch. 2.7 - Prob. 13E Ch. 2.7 - Prob. 14E Ch. 2.7 - Prob. 15E Ch. 2.7 - Prob. 16E Ch. 2.7 - Prob. 17E Ch. 2.7 - Prob. 18E Ch. 2.7 - Prob. 19E Ch. 2.7 - Prob. 20E Ch. 2.7 - Prob. 21E Ch. 2.7 - Prob. 22E Ch. 2.7 - Prob. 23E Ch. 2.7 - Prob. 24E Ch. 2.7 - Prob. 25E Ch. 2.7 - Prob. 26E Ch. 2.7 - Prob. 27E Ch. 2.7 - Prob. 28E Ch. 2.7 - Prob. 29E Ch. 2.7 - Prob. 30E Ch. 2.7 - Prob. 31E Ch. 2.7 - Prob. 32E Ch. 2.7 - Prob. 33E Ch. 2.7 - Prob. 34E Ch. 2.7 - Prob. 35E Ch. 2.7 - Prob. 36E Ch. 2.7 - Prob. 37E Ch. 2.7 - Prob. 38E Ch. 2.7 - Prob. 39E Ch. 2.7 - Prob. 40E Ch. 2.7 - Prob. 41E Ch. 2.7 - Prob. 42E Ch. 2.7 - Prob. 43E Ch. 2.7 - Prob. 44E Ch. 2.7 - Prob. 45E Ch. 2.7 - Prob. 46E Ch. 2.7 - Prob. 47E Ch. 2.7 - Prob. 48E Ch. 2.7 - Prob. 49E Ch. 2.7 - Prob. 50E Ch. 2.7 - Prob. 51E Ch. 2.7 - Prob. 52E Ch. 2.7 - Prob. 53E Ch. 2.7 - Prob. 54E Ch. 2.7 - Prob. 55E Ch. 2.7 - Prob. 56E Ch. 2.7 - Prob. 57E Ch. 2.7 - Prob. 58E Ch. 2.7 - Prob. 59E Ch. 2.7 - Prob. 60E Ch. 2.7 - Prob. 61E Ch. 2.7 - Prob. 62E Ch. 2.7 - Prob. 63E Ch. 2.7 - Prob. 64E Ch. 2.7 - Prob. 65E Ch. 2.7 - Prob. 66E Ch. 2.7 - Prob. 67E Ch. 2.7 - Prob. 68E Ch. 2.7 - Prob. 69E Ch. 2.7 - Prob. 70E Ch. 2.7 - Prob. 71E Ch. 2.7 - Prob. 72E Ch. 2.7 - Prob. 73E Ch. 2.7 - Prob. 74E Ch. 2.7 - Prob. 75E Ch. 2.7 - Prob. 76E Ch. 2.7 - Prob. 77E Ch. 2.7 - Prob. 78E Ch. 2.7 - Prob. 79E Ch. 2.7 - Prob. 80E Ch. 2.7 - Prob. 81E Ch. 2.7 - Prob. 82E Ch. 2.7 - Prob. 83E Ch. 2.7 - Prob. 84E Ch. 2.7 - Prob. 85E Ch. 2.7 - Prob. 86E Ch. 2.7 - Prob. 87E Ch. 2.7 - Prob. 88E Ch. 2.7 - Prob. 89E Ch. 2.7 - Prob. 90E Ch. 2 - Prob. 1RE Ch. 2 - Prob. 2RE Ch. 2 - Prob. 3RE Ch. 2 - Prob. 4RE Ch. 2 - Prob. 5RE Ch. 2 - Prob. 6RE Ch. 2 - Prob. 7RE Ch. 2 - Prob. 8RE Ch. 2 - Prob. 9RE Ch. 2 - Prob. 10RE Ch. 2 - Prob. 11RE Ch. 2 - Prob. 12RE Ch. 2 - Prob. 13RE Ch. 2 - Prob. 14RE Ch. 2 - Prob. 15RE Ch. 2 - Prob. 16RE Ch. 2 - Prob. 17RE Ch. 2 - Prob. 18RE Ch. 2 - Prob. 19RE Ch. 2 - Prob. 20RE Ch. 2 - Prob. 21RE Ch. 2 - Prob. 22RE Ch. 2 - Prob. 23RE Ch. 2 - Prob. 24RE Ch. 2 - Prob. 25RE Ch. 2 - Prob. 26RE Ch. 2 - Prob. 27RE Ch. 2 - Prob. 28RE Ch. 2 - Prob. 29RE Ch. 2 - Prob. 30RE Ch. 2 - Prob. 31RE Ch. 2 - Prob. 32RE Ch. 2 - Prob. 33RE Ch. 2 - Prob. 34RE Ch. 2 - Prob. 35RE Ch. 2 - Prob. 36RE Ch. 2 - Prob. 37RE Ch. 2 - Prob. 38RE Ch. 2 - Prob. 39RE Ch. 2 - Prob. 40RE Ch. 2 - Prob. 41RE Ch. 2 - Prob. 42RE Ch. 2 - Prob. 43RE Ch. 2 - Prob. 44RE Ch. 2 - Prob. 45RE Ch. 2 - Prob. 46RE Ch. 2 - Prob. 47RE Ch. 2 - Prob. 48RE Ch. 2 - Prob. 49RE Ch. 2 - Prob. 50RE Ch. 2 - Prob. 51RE Ch. 2 - Prob. 52RE Ch. 2 - Prob. 53RE Ch. 2 - Prob. 54RE Ch. 2 - Prob. 55RE Ch. 2 - Prob. 56RE Ch. 2 - Prob. 57RE Ch. 2 - Prob. 58RE Ch. 2 - Prob. 59RE Ch. 2 - Prob. 60RE Ch. 2 - Prob. 61RE Ch. 2 - Prob. 62RE Ch. 2 - Prob. 63RE Ch. 2 - Prob. 64RE Ch. 2 - Prob. 65RE Ch. 2 - Prob. 66RE Ch. 2 - Prob. 67RE Ch. 2 - Prob. 68RE Ch. 2 - Prob. 1CT Ch. 2 - Prob. 2CT Ch. 2 - Prob. 3CT Ch. 2 - Prob. 4CT Ch. 2 - Prob. 5CT Ch. 2 - Prob. 6CT Ch. 2 - Prob. 7CT Ch. 2 - Prob. 8CT Ch. 2 - Prob. 9CT Ch. 2 - Prob. 10CT Ch. 2 - Prob. 11CT Ch. 2 - Prob. 12CT Ch. 2 - Prob. 13CT Ch. 2 - Prob. 14CT Ch. 2 - Prob. 15CT Ch. 2 - Prob. 16CT Ch. 2 - Prob. 17CT Ch. 2 - Prob. 18CT Ch. 2 - Prob. 1PS Ch. 2 - Prob. 2PS Ch. 2 - Prob. 3PS Ch. 2 - Prob. 4PS Ch. 2 - Prob. 5PS Ch. 2 - Prob. 6PS Ch. 2 - Prob. 7PS Ch. 2 - Prob. 8PS Ch. 2 - Prob. 9PS Ch. 2 - Prob. 10PS Ch. 2 - Prob. 11PS Ch. 2 - Prob. 12PS Ch. 2 - Prob. 13PS

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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY

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Verify the given factor(s) of f(x) .

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Chapter 2 Solutions