Explanation Given information: The equation, 6 x ( x 2 + 1 ) 2 ( x 2 + 2 ) 4 − 8 x ( x 2 + 1 ) 3 ( x 2 + 2 ) 3 ( x 2 + 2 ) 8 = 0 . Formula used: Zero product property, If a product of two number is zero, one of the two must be zero. Condition to solve an equation of the form P Q = 0 , If P Q = 0 , then P = 0 . Calculation: Consider the expression, 6 x ( x 2 + 1 ) 2 ( x 2 + 2 ) 4 − 8 x ( x 2 + 1 ) 3 ( x 2 + 2 ) 3 ( x 2 + 2 ) 8 = 0 As the above equation is in P Q = 0 form. Therefore, the equation will be 6 x ( x 2 + 1 ) 2 ( x 2 + 2 ) 4 − 8 x ( x 2 + 1 ) 3 ( x 2 + 2 ) 3 = 0 . As both the term contains the term 2 x ( x 2 + 1 ) 2 ( x 2 + 2 ) 3 . Thus, the common factor is 2 x ( x 2 + 1 ) 2 ( x 2 + 2 ) 3 . Now, factor out the common factor and simplify as below, 6 x ( x 2 + 1 ) 2 ( x 2 + 2 ) 4 − 8 x ( x 2 + 1 ) 3 ( x 2 + 2 ) 3 = 0 2 x ( x 2 + 1 ) 2 ( x 2 + 2 ) 3 ( 3 ( x 2 + 2 ) − 4 ( x 2 + 1 ) ) = 0 2 x ( x 2 + 1 ) 2 ( <

7th Edition

ISBN: 9781337514309

Author: Waner

Publisher: Cengage

See similar textbooks

Videos

Question

Chapter 0.6, Problem 16E

To determine

To calculate: The solution of the equation 6x(x2+1)2(x2+2)4−8x(x2+1)3(x2+2)3(x2+2)8=0.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 0.6, Problem 15E

Chapter 0.6, Problem 17E

Students have asked these similar questions

The spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.

Find the indefinite integral. Check Answer: 7x 4 + 1x dx

show sketch

Chapter 0 Solutions

Applied Calculus

Ch. 0.1 - Prob. 1E Ch. 0.1 - Prob. 2E Ch. 0.1 - Prob. 3E Ch. 0.1 - Prob. 4E Ch. 0.1 - Prob. 5E Ch. 0.1 - Prob. 6E Ch. 0.1 - Prob. 7E Ch. 0.1 - Prob. 8E Ch. 0.1 - Prob. 9E Ch. 0.1 - Prob. 10E

Ch. 0.1 - Prob. 11E Ch. 0.1 - Prob. 12E Ch. 0.1 - Prob. 13E Ch. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Prob. 15E Ch. 0.1 - Prob. 16E Ch. 0.1 - Calculate each expression in Exercises 124, giving...Ch. 0.1 - Prob. 18E Ch. 0.1 - Prob. 19E Ch. 0.1 - Prob. 20E Ch. 0.1 - Prob. 21E Ch. 0.1 - Prob. 22E Ch. 0.1 - Prob. 23E Ch. 0.1 - Prob. 24E Ch. 0.1 - Prob. 25E Ch. 0.1 - Prob. 26E Ch. 0.1 - Prob. 27E Ch. 0.1 - Prob. 28E Ch. 0.1 - Prob. 29E Ch. 0.1 - Prob. 30E Ch. 0.1 - Prob. 31E Ch. 0.1 - Prob. 32E Ch. 0.1 - Prob. 33E Ch. 0.1 - Prob. 34E Ch. 0.1 - Prob. 35E Ch. 0.1 - Prob. 36E Ch. 0.1 - Convert each expression in Exercises 25-50 into...Ch. 0.1 - Prob. 38E Ch. 0.1 - Prob. 39E Ch. 0.1 - Prob. 40E Ch. 0.1 - Prob. 41E Ch. 0.1 - Prob. 42E Ch. 0.1 - Prob. 43E Ch. 0.1 - Prob. 44E Ch. 0.1 - Prob. 45E Ch. 0.1 - Prob. 46E Ch. 0.1 - Prob. 47E Ch. 0.1 - Prob. 48E Ch. 0.1 - Prob. 49E Ch. 0.1 - Prob. 50E Ch. 0.2 - Evaluate the expression sin Exercises 116. 33 Ch. 0.2 - Prob. 2E Ch. 0.2 - Evaluate the expression sin Exercises 116. (23)2 Ch. 0.2 - Prob. 4E Ch. 0.2 - Prob. 5E Ch. 0.2 - Prob. 6E Ch. 0.2 - Prob. 7E Ch. 0.2 - Prob. 8E Ch. 0.2 - Prob. 9E Ch. 0.2 - Prob. 10E Ch. 0.2 - Prob. 11E Ch. 0.2 - Prob. 12E Ch. 0.2 - Prob. 13E Ch. 0.2 - Prob. 14E Ch. 0.2 - Prob. 15E Ch. 0.2 - Prob. 16E Ch. 0.2 - Prob. 17E Ch. 0.2 - Prob. 18E Ch. 0.2 - Prob. 19E Ch. 0.2 - Prob. 20E Ch. 0.2 - Prob. 21E Ch. 0.2 - Prob. 22E Ch. 0.2 - Prob. 23E Ch. 0.2 - Prob. 24E Ch. 0.2 - Prob. 25E Ch. 0.2 - Prob. 26E Ch. 0.2 - Prob. 27E Ch. 0.2 - Prob. 28E Ch. 0.2 - Prob. 29E Ch. 0.2 - Prob. 30E Ch. 0.2 - Prob. 31E Ch. 0.2 - Prob. 32E Ch. 0.2 - Prob. 33E Ch. 0.2 - Prob. 34E Ch. 0.2 - Prob. 35E Ch. 0.2 - Prob. 36E Ch. 0.2 - Prob. 37E Ch. 0.2 - Prob. 38E Ch. 0.2 - Prob. 39E Ch. 0.2 - Prob. 40E Ch. 0.2 - Prob. 41E Ch. 0.2 - Prob. 42E Ch. 0.2 - Prob. 43E Ch. 0.2 - Prob. 44E Ch. 0.2 - Prob. 45E Ch. 0.2 - Evaluate expressions in Exercises 3756, rounding...Ch. 0.2 - Prob. 47E Ch. 0.2 - Prob. 48E Ch. 0.2 - Prob. 49E Ch. 0.2 - Prob. 50E Ch. 0.2 - Prob. 51E Ch. 0.2 - Prob. 52E Ch. 0.2 - Prob. 53E Ch. 0.2 - Prob. 54E Ch. 0.2 - Prob. 55E Ch. 0.2 - Prob. 56E Ch. 0.2 - Prob. 57E Ch. 0.2 - Prob. 58E Ch. 0.2 - Prob. 59E Ch. 0.2 - Prob. 60E Ch. 0.2 - Prob. 61E Ch. 0.2 - Prob. 62E Ch. 0.2 - Prob. 63E Ch. 0.2 - Prob. 64E Ch. 0.2 - Prob. 65E Ch. 0.2 - Prob. 66E Ch. 0.2 - Prob. 67E Ch. 0.2 - Prob. 68E Ch. 0.2 - Prob. 69E Ch. 0.2 - Prob. 70E Ch. 0.2 - Prob. 71E Ch. 0.2 - Prob. 72E Ch. 0.2 - Prob. 73E Ch. 0.2 - Prob. 74E Ch. 0.2 - Prob. 75E Ch. 0.2 - Prob. 76E Ch. 0.2 - Prob. 77E Ch. 0.2 - Prob. 78E Ch. 0.2 - Prob. 79E Ch. 0.2 - Prob. 80E Ch. 0.2 - Prob. 81E Ch. 0.2 - Prob. 82E Ch. 0.2 - Prob. 83E Ch. 0.2 - Prob. 84E Ch. 0.2 - Prob. 85E Ch. 0.2 - Prob. 86E Ch. 0.2 - Prob. 87E Ch. 0.2 - Prob. 88E Ch. 0.2 - Prob. 89E Ch. 0.2 - Prob. 90E Ch. 0.2 - Prob. 91E Ch. 0.2 - Prob. 92E Ch. 0.2 - Prob. 93E Ch. 0.2 - Prob. 94E Ch. 0.2 - Prob. 95E Ch. 0.2 - Prob. 96E Ch. 0.2 - Prob. 97E Ch. 0.2 - Prob. 98E Ch. 0.2 - Prob. 99E Ch. 0.2 - Prob. 100E Ch. 0.2 - Prob. 101E Ch. 0.2 - Prob. 102E Ch. 0.2 - Prob. 103E Ch. 0.2 - Prob. 104E Ch. 0.2 - Prob. 105E Ch. 0.2 - Prob. 106E Ch. 0.2 - Prob. 107E Ch. 0.2 - Prob. 108E Ch. 0.2 - Prob. 109E Ch. 0.2 - Prob. 110E Ch. 0.2 - Prob. 111E Ch. 0.2 - Prob. 112E Ch. 0.2 - Prob. 113E Ch. 0.2 - Prob. 114E Ch. 0.2 - Prob. 115E Ch. 0.2 - Prob. 116E Ch. 0.2 - Prob. 117E Ch. 0.2 - Prob. 118E Ch. 0.2 - Prob. 119E Ch. 0.2 - Prob. 120E Ch. 0.3 - Expand each expression in Exercises 122. x(4x+6)Ch. 0.3 - Prob. 2E Ch. 0.3 - Prob. 3E Ch. 0.3 - Prob. 4E Ch. 0.3 - Prob. 5E Ch. 0.3 - Prob. 6E Ch. 0.3 - Prob. 7E Ch. 0.3 - Prob. 8E Ch. 0.3 - Prob. 9E Ch. 0.3 - Prob. 10E Ch. 0.3 - Prob. 11E Ch. 0.3 - Prob. 12E Ch. 0.3 - Prob. 13E Ch. 0.3 - Prob. 14E Ch. 0.3 - Prob. 15E Ch. 0.3 - Prob. 16E Ch. 0.3 - Prob. 17E Ch. 0.3 - Prob. 18E Ch. 0.3 - Prob. 19E Ch. 0.3 - Prob. 20E Ch. 0.3 - Prob. 21E Ch. 0.3 - Prob. 22E Ch. 0.3 - Prob. 23E Ch. 0.3 - Prob. 24E Ch. 0.3 - Prob. 25E Ch. 0.3 - Prob. 26E Ch. 0.3 - Prob. 27E Ch. 0.3 - Prob. 28E Ch. 0.3 - Prob. 29E Ch. 0.3 - Prob. 30E Ch. 0.3 - Prob. 31E Ch. 0.3 - Prob. 32E Ch. 0.3 - Prob. 33E Ch. 0.3 - Prob. 34E Ch. 0.3 - Prob. 35E Ch. 0.3 - Prob. 36E Ch. 0.3 - Prob. 37E Ch. 0.3 - Prob. 38E Ch. 0.3 - In Exercises 3148, (a) factor the given...Ch. 0.3 - Prob. 40E Ch. 0.3 - Prob. 41E Ch. 0.3 - Prob. 42E Ch. 0.3 - Prob. 43E Ch. 0.3 - Prob. 44E Ch. 0.3 - Prob. 45E Ch. 0.3 - Prob. 46E Ch. 0.3 - Prob. 47E Ch. 0.3 - Prob. 48E Ch. 0.4 - Rewrite each expression in Exercises 116 as a...Ch. 0.4 - Prob. 2E Ch. 0.4 - Prob. 3E Ch. 0.4 - Prob. 4E Ch. 0.4 - Prob. 5E Ch. 0.4 - Prob. 6E Ch. 0.4 - Prob. 7E Ch. 0.4 - Prob. 8E Ch. 0.4 - Prob. 9E Ch. 0.4 - Prob. 10E Ch. 0.4 - Prob. 11E Ch. 0.4 - Rewrite each expression in Exercises 116 as a...Ch. 0.4 - Prob. 13E Ch. 0.4 - Prob. 14E Ch. 0.4 - Prob. 15E Ch. 0.4 - Prob. 16E Ch. 0.5 - Prob. 1E Ch. 0.5 - Prob. 2E Ch. 0.5 - Prob. 3E Ch. 0.5 - Prob. 4E Ch. 0.5 - Prob. 5E Ch. 0.5 - Prob. 6E Ch. 0.5 - Prob. 7E Ch. 0.5 - Prob. 8E Ch. 0.5 - Prob. 9E Ch. 0.5 - Prob. 10E Ch. 0.5 - Prob. 11E Ch. 0.5 - Prob. 12E Ch. 0.5 - Prob. 13E Ch. 0.5 - Prob. 14E Ch. 0.5 - By any method, determine all possible real...Ch. 0.5 - Prob. 16E Ch. 0.5 - Prob. 17E Ch. 0.5 - Prob. 18E Ch. 0.5 - Prob. 19E Ch. 0.5 - Prob. 20E Ch. 0.5 - Prob. 21E Ch. 0.5 - Prob. 22E Ch. 0.5 - Prob. 23E Ch. 0.5 - Prob. 24E Ch. 0.5 - Prob. 25E Ch. 0.5 - Prob. 26E Ch. 0.5 - Prob. 27E Ch. 0.5 - Prob. 28E Ch. 0.5 - Prob. 29E Ch. 0.5 - Prob. 30E Ch. 0.5 - Prob. 31E Ch. 0.5 - Prob. 32E Ch. 0.5 - Prob. 33E Ch. 0.5 - Prob. 34E Ch. 0.5 - Prob. 35E Ch. 0.5 - Prob. 36E Ch. 0.5 - Prob. 37E Ch. 0.5 - Prob. 38E Ch. 0.5 - Prob. 39E Ch. 0.5 - Prob. 40E Ch. 0.5 - Prob. 41E Ch. 0.5 - Prob. 42E Ch. 0.5 - Prob. 43E Ch. 0.5 - Prob. 44E Ch. 0.6 - Solve the equations in Exercises 126. x43x3=0 Ch. 0.6 - Prob. 2E Ch. 0.6 - Prob. 3E Ch. 0.6 - Prob. 4E Ch. 0.6 - Prob. 5E Ch. 0.6 - Prob. 6E Ch. 0.6 - Prob. 7E Ch. 0.6 - Prob. 8E Ch. 0.6 - Prob. 9E Ch. 0.6 - Prob. 10E Ch. 0.6 - Prob. 11E Ch. 0.6 - Prob. 12E Ch. 0.6 - Prob. 13E Ch. 0.6 - Prob. 14E Ch. 0.6 - Prob. 15E Ch. 0.6 - Prob. 16E Ch. 0.6 - Prob. 17E Ch. 0.6 - Prob. 18E Ch. 0.6 - Prob. 19E Ch. 0.6 - Prob. 20E Ch. 0.6 - Prob. 21E Ch. 0.6 - Prob. 22E Ch. 0.6 - Prob. 23E Ch. 0.6 - Prob. 24E Ch. 0.6 - Prob. 25E Ch. 0.6 - Solve the equations in Exercises 126. 2x3x2x3x+1=0 Ch. 0.7 - Prob. 1E Ch. 0.7 - Prob. 2E Ch. 0.7 - Prob. 3E Ch. 0.7 - Prob. 4E Ch. 0.7 - Prob. 5E Ch. 0.7 - Prob. 6E Ch. 0.7 - Prob. 7E Ch. 0.7 - Prob. 8E Ch. 0.7 - Sketch the graphs of the equations in Exercises...Ch. 0.7 - Prob. 10E Ch. 0.7 - Prob. 11E Ch. 0.7 - Prob. 12E Ch. 0.7 - Prob. 13E Ch. 0.7 - Prob. 14E Ch. 0.7 - Prob. 15E Ch. 0.7 - Prob. 16E Ch. 0.7 - Find the value of k such that (1,k) is equidistant...Ch. 0.7 - Find the value of k such that (k,k) is equidistant...Ch. 0.7 - Prob. 19E Ch. 0.7 - Describe the set of points (x,y) such that...Ch. 0.8 - Prob. 1E Ch. 0.8 - Prob. 2E Ch. 0.8 - Prob. 3E Ch. 0.8 - Prob. 4E Ch. 0.8 - Prob. 5E Ch. 0.8 - Prob. 6E Ch. 0.8 - Prob. 7E Ch. 0.8 - Prob. 8E Ch. 0.8 - Prob. 9E Ch. 0.8 - Prob. 10E Ch. 0.8 - Prob. 11E Ch. 0.8 - Prob. 12E Ch. 0.8 - Prob. 13E Ch. 0.8 - Prob. 14E Ch. 0.8 - Prob. 15E Ch. 0.8 - Prob. 16E Ch. 0.8 - Prob. 17E Ch. 0.8 - Prob. 18E Ch. 0.8 - Prob. 19E Ch. 0.8 - Prob. 20E Ch. 0.8 - Prob. 21E Ch. 0.8 - Prob. 22E Ch. 0.8 - Prob. 23E Ch. 0.8 - In Exercises 1728, use the logarithm identities to...Ch. 0.8 - Prob. 25E Ch. 0.8 - Prob. 26E Ch. 0.8 - Prob. 27E Ch. 0.8 - Prob. 28E Ch. 0.8 - Prob. 29E Ch. 0.8 - Prob. 30E Ch. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - Prob. 32E Ch. 0.8 - Let a=log2,b=log3, and c=log7. In Exercises 2946,...Ch. 0.8 - Prob. 34E Ch. 0.8 - Prob. 35E Ch. 0.8 - Prob. 36E Ch. 0.8 - Prob. 37E Ch. 0.8 - Prob. 38E Ch. 0.8 - Prob. 39E Ch. 0.8 - Prob. 40E Ch. 0.8 - Prob. 41E Ch. 0.8 - Prob. 42E Ch. 0.8 - Prob. 43E Ch. 0.8 - Prob. 44E Ch. 0.8 - Prob. 45E Ch. 0.8 - Prob. 46E Ch. 0.8 - Prob. 47E Ch. 0.8 - Prob. 48E Ch. 0.8 - Prob. 49E Ch. 0.8 - Prob. 50E Ch. 0.8 - Prob. 51E Ch. 0.8 - Prob. 52E Ch. 0.8 - Prob. 53E Ch. 0.8 - Prob. 54E Ch. 0.8 - Prob. 55E Ch. 0.8 - Prob. 56E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The solution of the equation 6 x ( x 2 + 1 ) 2 ( x 2 + 2 ) 4 − 8 x ( x 2 + 1 ) 3 ( x 2 + 2 ) 3 ( x 2 + 2 ) 8 = 0 .

Solution Summary: The author explains the formula used to solve an equation of the form PQ=0.

Videos

To calculate: The solution of the equation 6x(x2+1)2(x2+2)4−8x(x2+1)3(x2+2)3(x2+2)8=0.

Want to see the full answer?

Chapter 0 Solutions