Explanation Procedure used: Rational Solutions Test: “The rational solutions of the polynomial equation a n x n + a n − 1 x n − 1 + ⋅ ⋅ ⋅ + a 1 x + a 0 = 0 with integer coefficients must be of the form p q , where p is a factor of the constant term a 0 and q is a factor of a n , the leading coefficient”. Calculation: The polynomial equation x 3 − 6 x 2 + 5 x + 12 = 0 . Use rational solution test, the rational solution of the equation x 3 − 6 x 2 + 5 x + 12 = 0 of the form p q where p is a factor of the constant term 12 and q is a factor of the leading coefficient 1. The factors of 12 are ± 1 , ± 2 , ± 3 , ± 4 , ± 6 , and ± 12

6th Edition

ISBN: 9780135823002

Author: HARSHBARGER

Publisher: PEARSON

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Chapter 6.4, Problem 17E

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To find: All possible rational solutions of the polynomial equation x3−6x2+5x+12=0.

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Chapter 6.4, Problem 16E

Chapter 6.4, Problem 18E

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Chapter 6 Solutions

MYLAB MATH COLLEGE ALGEBRA IN CONTEXT

Ch. 6.1 - Graph the function h(x) = 3x3 + 5x2 x 10 on the...Ch. 6.1 - Graph the function f(x) = 2x3 3x2 6x on the...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - For Exercises 1116, match the polynomial function...Ch. 6.1 - For Exercises 1720, use the equation of the...Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Sketch a graph of any cubic polynomial function...Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Daily Revenue The daily revenue in dollars from...Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Starbucks Using data from 2005 and projected to...Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Salaries The median salary for male workers, in...Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.2 - Find the cubic function that models the data in...Ch. 6.2 - Find the cubic function that is the best fit for...Ch. 6.2 - Prob. 3E Ch. 6.2 - Find the quartic function that is the best fit for...Ch. 6.2 - Prob. 5E Ch. 6.2 - a. Make a scatter plot of the data in the table...Ch. 6.2 - Prob. 7E Ch. 6.2 - a. Find a cubic function that models the data in...Ch. 6.2 - Prob. 9E Ch. 6.2 - a. Graph each of the functions found in Exercise 9...Ch. 6.2 - Prob. 11E Ch. 6.2 - Prob. 12E Ch. 6.2 - Prob. 13E Ch. 6.2 - Prob. 14E Ch. 6.2 - Prob. 15E Ch. 6.2 - Find the cubic function that is the best fit for...Ch. 6.2 - Use unrounded models for graphing and calculations...Ch. 6.2 - Use unrounded models for graphing and calculations...Ch. 6.2 - Prob. 19E Ch. 6.2 - Prob. 20E Ch. 6.2 - Median Age at First Marriage (Source: U.S. Census...Ch. 6.2 - Prob. 22E Ch. 6.2 - Prob. 23E Ch. 6.2 - Inflation Rate The annual changes in the consumer...Ch. 6.2 - Elderly Men in the Workforce The table below gives...Ch. 6.2 - Prob. 26E Ch. 6.2 - Prob. 27E Ch. 6.2 - Consumer Prices The data in the table give the...Ch. 6.2 - Federal Tax Per Capita The table gives the amount...Ch. 6.2 - Japanese Economy The economy of Japan is the third...Ch. 6.2 - Women in the Workforce The following table gives...Ch. 6.2 - Homicide Rates The table gives the U.S. homicide...Ch. 6.2 - Prob. 33E Ch. 6.2 - Prob. 34E Ch. 6.2 - Prob. 35E Ch. 6.2 - Union Membership The table on the next page gives...Ch. 6.2 - Prob. 37E Ch. 6.2 - Medicaid The numbers of thousands of people...Ch. 6.3 - Prob. 1E Ch. 6.3 - Prob. 2E Ch. 6.3 - Prob. 3E Ch. 6.3 - Prob. 4E Ch. 6.3 - Prob. 5E Ch. 6.3 - Prob. 6E Ch. 6.3 - Prob. 7E Ch. 6.3 - Prob. 8E Ch. 6.3 - Prob. 9E Ch. 6.3 - Prob. 10E Ch. 6.3 - Prob. 11E Ch. 6.3 - Prob. 12E Ch. 6.3 - Prob. 13E Ch. 6.3 - Prob. 14E Ch. 6.3 - Prob. 15E Ch. 6.3 - Prob. 16E Ch. 6.3 - Prob. 17E Ch. 6.3 - Prob. 18E Ch. 6.3 - Prob. 19E Ch. 6.3 - Prob. 20E Ch. 6.3 - Prob. 21E Ch. 6.3 - Prob. 22E Ch. 6.3 - Prob. 23E Ch. 6.3 - Prob. 24E Ch. 6.3 - Prob. 25E Ch. 6.3 - Prob. 26E Ch. 6.3 - Prob. 27E Ch. 6.3 - Prob. 28E Ch. 6.3 - Prob. 29E Ch. 6.3 - Prob. 30E Ch. 6.3 - Prob. 31E Ch. 6.3 - Prob. 32E Ch. 6.3 - Prob. 33E Ch. 6.3 - Prob. 34E Ch. 6.3 - Prob. 35E Ch. 6.3 - Prob. 36E Ch. 6.3 - Prob. 37E Ch. 6.3 - Prob. 38E Ch. 6.3 - Constructing a Box A box can be formed by cutting...Ch. 6.3 - Prob. 40E Ch. 6.3 - Prob. 41E Ch. 6.3 - Prob. 42E Ch. 6.3 - Prob. 43E Ch. 6.3 - Prob. 44E Ch. 6.3 - Prob. 45E Ch. 6.3 - Prob. 46E Ch. 6.3 - Prob. 47E Ch. 6.3 - Prob. 48E Ch. 6.3 - Prob. 49E Ch. 6.3 - Prob. 50E Ch. 6.4 - In Exercises 14, use synthetic division to find...Ch. 6.4 - Prob. 2E Ch. 6.4 - Prob. 3E Ch. 6.4 - Prob. 4E Ch. 6.4 - Prob. 5E Ch. 6.4 - Prob. 6E Ch. 6.4 - Prob. 7E Ch. 6.4 - Prob. 8E Ch. 6.4 - Prob. 9E Ch. 6.4 - Prob. 10E Ch. 6.4 - Prob. 11E Ch. 6.4 - Prob. 12E Ch. 6.4 - Prob. 13E Ch. 6.4 - Prob. 14E Ch. 6.4 - In Exercises 1316, find one solution graphically...Ch. 6.4 - Prob. 16E Ch. 6.4 - Prob. 17E Ch. 6.4 - Prob. 18E Ch. 6.4 - Prob. 19E Ch. 6.4 - Prob. 20E Ch. 6.4 - Prob. 21E Ch. 6.4 - Prob. 22E Ch. 6.4 - Prob. 23E Ch. 6.4 - In Exercises 2124, find all rational zeros of the...Ch. 6.4 - Prob. 25E Ch. 6.4 - Prob. 26E Ch. 6.4 - Prob. 27E Ch. 6.4 - Solve each of the equations in Exercises 2530...Ch. 6.4 - Prob. 29E Ch. 6.4 - Prob. 30E Ch. 6.4 - Prob. 31E Ch. 6.4 - In Exercises 3136, use synthetic division and...Ch. 6.4 - Prob. 33E Ch. 6.4 - Prob. 34E Ch. 6.4 - Prob. 35E Ch. 6.4 - Prob. 36E Ch. 6.4 - Drunk Driving Crashes Suppose the total number of...Ch. 6.4 - Prob. 38E Ch. 6.4 - Prob. 39E Ch. 6.4 - Births The number of births to females in the...Ch. 6.4 - Prob. 41E Ch. 6.4 - Personal Savings The model y = 0.000447x3 ...Ch. 6.5 - Give the equations of any (a) vertical and (b)...Ch. 6.5 - Prob. 2E Ch. 6.5 - Prob. 3E Ch. 6.5 - Prob. 4E Ch. 6.5 - Prob. 5E Ch. 6.5 - Prob. 6E Ch. 6.5 - Prob. 7E Ch. 6.5 - Prob. 8E Ch. 6.5 - Prob. 9E Ch. 6.5 - Prob. 10E Ch. 6.5 - Prob. 11E Ch. 6.5 - Prob. 12E Ch. 6.5 - Prob. 13E Ch. 6.5 - Prob. 14E Ch. 6.5 - Prob. 15E Ch. 6.5 - Prob. 16E Ch. 6.5 - Prob. 17E Ch. 6.5 - Prob. 18E Ch. 6.5 - Prob. 19E Ch. 6.5 - Prob. 20E Ch. 6.5 - Prob. 21E Ch. 6.5 - Prob. 22E Ch. 6.5 - Prob. 23E Ch. 6.5 - Prob. 24E Ch. 6.5 - Prob. 25E Ch. 6.5 - Prob. 26E Ch. 6.5 - Prob. 27E Ch. 6.5 - Prob. 28E Ch. 6.5 - Prob. 29E Ch. 6.5 - Prob. 30E Ch. 6.5 - Prob. 31E Ch. 6.5 - Prob. 32E Ch. 6.5 - Prob. 33E Ch. 6.5 - Prob. 34E Ch. 6.5 - Prob. 35E Ch. 6.5 - Prob. 36E Ch. 6.5 - Prob. 37E Ch. 6.5 - Prob. 38E Ch. 6.5 - Prob. 39E Ch. 6.5 - Prob. 40E Ch. 6.5 - Prob. 41E Ch. 6.5 - Average Cost The average cost per unit for the...Ch. 6.5 - Prob. 43E Ch. 6.5 - Prob. 44E Ch. 6.5 - Prob. 45E Ch. 6.5 - Prob. 46E Ch. 6.5 - Prob. 47E Ch. 6.5 - Prob. 48E Ch. 6.5 - Prob. 49E Ch. 6.5 - Prob. 50E Ch. 6.5 - Prob. 51E Ch. 6.5 - Prob. 52E Ch. 6.5 - Prob. 53E Ch. 6.5 - Prob. 54E Ch. 6.5 - Age at First Marriage The table that follows shows...Ch. 6.5 - Fences Suppose that a rectangular field is to have...Ch. 6.5 - Prob. 57E Ch. 6.5 - Prob. 58E Ch. 6.6 - Prob. 1E Ch. 6.6 - Prob. 2E Ch. 6.6 - Prob. 3E Ch. 6.6 - Prob. 4E Ch. 6.6 - In Exercises 116, use algebraic and/or graphical...Ch. 6.6 - Prob. 6E Ch. 6.6 - Prob. 7E Ch. 6.6 - Prob. 8E Ch. 6.6 - Prob. 9E Ch. 6.6 - Prob. 10E Ch. 6.6 - Prob. 11E Ch. 6.6 - Prob. 12E Ch. 6.6 - Prob. 13E Ch. 6.6 - Prob. 14E Ch. 6.6 - Prob. 15E Ch. 6.6 - Prob. 16E Ch. 6.6 - For Exercises 1720, use the graph of y = f(x) to...Ch. 6.6 - Prob. 18E Ch. 6.6 - Prob. 19E Ch. 6.6 - Prob. 20E Ch. 6.6 - Prob. 21E Ch. 6.6 - Prob. 22E Ch. 6.6 - Prob. 23E Ch. 6.6 - Prob. 24E Ch. 6.6 - Prob. 25E Ch. 6.6 - Combine factoring with graphical and/or numerical...Ch. 6.6 - Prob. 27E Ch. 6.6 - 28. Average Cost The average cost per set for the...Ch. 6.6 - Prob. 29E Ch. 6.6 - Prob. 30E Ch. 6.6 - Prob. 31E Ch. 6.6 - Prob. 32E Ch. 6.6 - Prob. 33E Ch. 6.6 - Prob. 34E Ch. 6.6 - Population Suppose the number of employees of a...Ch. 6 - For Exercises 14, (a) give the degree of the...Ch. 6 - For Exercises 14, (a) give the degree of the...Ch. 6 - Prob. 3TE Ch. 6 - Prob. 4TE Ch. 6 - Prob. 5TE Ch. 6 - Prob. 6TE Ch. 6 - Prob. 7TE Ch. 6 - Prob. 8TE Ch. 6 - Prob. 9TE Ch. 6 - Prob. 10TE Ch. 6 - Prob. 11TE Ch. 6 - Prob. 12TE Ch. 6 - Prob. 13TE Ch. 6 - Prob. 14TE Ch. 6 - In Exercises 1116, simplify each rational...Ch. 6 - Prob. 16TE Ch. 6 - Prob. 17TE Ch. 6 - Prob. 18TE Ch. 6 - Prob. 19TE Ch. 6 - Prob. 20TE Ch. 6 - Prob. 21TE Ch. 6 - Prob. 22TE Ch. 6 - Prob. 23TE Ch. 6 - Prob. 24TE Ch. 6 - Prob. 25TE Ch. 6 - Prob. 26TE Ch. 6 - Prob. 27TE Ch. 6 - Prob. 28TE Ch. 6 - Prob. 29TE Ch. 6 - Prob. 30TE Ch. 6 - Prob. 31TE Ch. 6 - Prob. 32TE Ch. 6 - Prob. 33TE Ch. 6 - Prob. 34TE Ch. 6 - Prob. 35TE Ch. 6 - Prob. 36TE Ch. 6 - Prob. 37TE Ch. 6 - Prob. 38TE Ch. 6 - Prob. 39TE Ch. 6 - Prob. 40TE Ch. 6 - In Exercises 3841, perform the long division. 41....Ch. 6 - Prob. 1RE Ch. 6 - Prob. 2RE Ch. 6 - Prob. 3RE Ch. 6 - Prob. 4RE Ch. 6 - Prob. 5RE Ch. 6 - Prob. 6RE Ch. 6 - Prob. 7RE Ch. 6 - Prob. 8RE Ch. 6 - Solve x4 x3 20x2 = 0.Ch. 6 - Prob. 10RE Ch. 6 - Prob. 11RE Ch. 6 - Prob. 12RE Ch. 6 - Prob. 13RE Ch. 6 - Prob. 14RE Ch. 6 - Prob. 15RE Ch. 6 - Prob. 16RE Ch. 6 - Prob. 17RE Ch. 6 - Prob. 18RE Ch. 6 - Find one solution of 3x3 x2 12x + 4 = 0...Ch. 6 - Find one solution of 2x3 + 5x2 4x 3 = 0...Ch. 6 - Prob. 21RE Ch. 6 - Prob. 22RE Ch. 6 - Prob. 23RE Ch. 6 - Prob. 24RE Ch. 6 - Prob. 25RE Ch. 6 - Prob. 26RE Ch. 6 - Prob. 27RE Ch. 6 - Prob. 28RE Ch. 6 - Prob. 29RE Ch. 6 - Prob. 30RE Ch. 6 - Prob. 31RE Ch. 6 - Prob. 32RE Ch. 6 - Prob. 33RE Ch. 6 - Revenue The monthly revenue for a product is given...Ch. 6 - Prob. 35RE Ch. 6 - Prob. 36RE Ch. 6 - Prob. 37RE Ch. 6 - Prob. 38RE Ch. 6 - Foreign Born Population The table on the following...Ch. 6 - Prob. 40RE Ch. 6 - Prob. 41RE Ch. 6 - Break-Even The daily profit in dollars for a...Ch. 6 - Starbucks The table gives the total number of...Ch. 6 - Drugs in the Bloodstream The concentration of a...Ch. 6 - Prob. 45RE Ch. 6 - Prob. 46RE Ch. 6 - Prob. 47RE Ch. 6 - Prob. 48RE Ch. 6 - Prob. 49RE Ch. 6 - Prob. 50RE Ch. 6 - Prob. 51RE Ch. 6 - Prob. 52RE Ch. 6 - Prob. 53RE Ch. 6 - Cost-Benefit The percent p of particulate...

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All possible rational solutions of the polynomial equation x 3 − 6 x 2 + 5 x + 12 = 0 .

Solution Summary: The author explains the rational solution of the polynomial equation x3-6+5x+12=0.

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To find: All possible rational solutions of the polynomial equation x3−6x2+5x+12=0.

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Chapter 6 Solutions