Explanation Given: The value of polynomial is given as P ( x ) = 8 x 5 − 14 x 4 − 22 x 3 + 57 x 2 − 35 x + 6 . Definition used: Rational zeros theorem is explained as for the polynomial P ( x ) = a n x n + a n − 1 x n − 1 + ⋯ a 1 x + a 0 with positive integer coefficient then the rational zeros of the P is in the form, P = p ( factor of constant term ) q ( factor of leading coefficent ) . Where, p is the factor of a 0 q is the factor for a n Factor theorem: For the polynomial P ( x ) , c is zero for P if ( x − c ) is the factor of P ( x ) . Then P ( x ) can be written as, P ( x ) = ( x − c ) Q ( x ) . Calculation: In the equation P ( x ) = 8 x 5 − 14 x 4 − 22 x 3 + 57 x 2 − 35 x + 6 , the constant term a 0 is 6 and the leading coefficient a n is 8. Use the rational zeros theorem. So, the number of zeros is, P = factor of 6 factor of 8 (1) The factors of 8 are ± 1 , ± 2 , ± 4 , ± 8 and the factors for 6 are ± 1 , ± 2 , ± 3 , ± 6 . Substitute these values in equation (1), So, the values of zeros of P are, ± 1 1 , ± 2 , ± 3 , ± 1 4 , ± 1 2 , ± 1 8 , ± 3 2 , ± 3 4 , ± 3 8 , ± 6 Further solve the fractions, ± 1 , ± 2 , ± 3 , ± 1 4 , ± 1 2 , ± 1 8 , ± 3 2 , ± 3 4 , ± 3 8 , ± 6 By the Descartes’ rule, The number of positive real zeros is equal to number of variation in sign in P ( x ) or less than that of a even whole number. So, there are 4 changes in sign so, the number of positive real zero is 4 or 4 − 2 = 2 Check the value − 2 by the synthetic division, − 2 8 − 14 − 22 57 − 35 6 − 16 60 − 76 38 − 6 8 − 30 38 − 19 3 0 The value − 2 is the zeros of the P ( x ) = 8 x 5 − 14 x 4 − 22 x 3 + 57 x 2 − 35 x + 6 . Use Factor theorem to solve the equation

Precalculus - Mathematics for Calculus - Seventh Edition

7th Edition

ISBN: 9781305750463

Author: Stewart

Publisher: CENGAGE C

See similar textbooks

Concept explainers

Quadratic Equation

When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations …

Demand and Supply Function

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to …

Videos

Question

Chapter 3.4, Problem 86E

To determine

The possible zeros of the polynomial P(x)=8x5−14x4−22x3+57x2−35x+6 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.4, Problem 85E

Chapter 3.4, Problem 87E

Students have asked these similar questions

Calculus III May I please have the example, definition semicolons, and all blanks completed and solved? Thank you so much,

A company estimates that the revenue (in dollars) from the sale of x doghouses is given by R(x) = 12,000 In (0.02x+1). Use the differential to approximate the change in revenue from the sale of one more doghouse if 80 doghouses have already been sold. The revenue will increase by $ if one more doghouse is made. (Round to the nearest cent as needed.)

The population of bacteria (in millions) in a certain culture x hours after an experimental 20x nutrient is introduced into the culture is P(x) = - 2 Use the differential to approximate the changes in population for the following changes in x. 8+x a. 1 to 1.5 b. 3 to 3.25 a. Use the differential to approximate the change in population for x=1 to 1.5. Between 1 and 1.5 hours, the population of bacteria changes by million. (Round to three decimal places as needed.)

Chapter 3 Solutions

Precalculus - Mathematics for Calculus - Seventh Edition

Ch. 3.1 - To put the quadratic function f(x)=ax2+bx+c in...Ch. 3.1 - The quadratic function f(x) = a(x - h)2 + k is in...Ch. 3.1 - The graph of f(x) = 3(x - 2)2 - 6 is a parabola...Ch. 3.1 - The graph of f(x) = -3(x - 2)2 - 6 is a parabola...Ch. 3.1 - Graphs of Quadratic Functions The graph of a...Ch. 3.1 - Graphs of Quadratic Functions The graph of a...Ch. 3.1 - Graphs of Quadratic Functions The graph of a...Ch. 3.1 - Graphs of Quadratic Functions The graph of a...Ch. 3.1 - Graphing Quadratic Functions A quadratic function...Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Graphing Quadratic Functions A quadratic function...Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Graphing Quadratic Functions A quadratic function...Ch. 3.1 - Graphing Quadratic Functions A quadratic function...Ch. 3.1 - Graphing Quadratic Functions A quadratic function...Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Maximum and Minimum Values A quadratic function f...Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Maximum and Minimum Values A quadratic function f...Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Maximum and Minimum Values A quadratic function f...Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Formula for Maximum and Minimum Values Find the...Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Formula for Maximum and Minimum Values Find the...Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Finding Quadratic Functions Find a function f...Ch. 3.1 - Finding Quadratic Functions Find a function f...Ch. 3.1 - Maximum of a Fourth-Degree Polynomial Find the...Ch. 3.1 - Maximum of a Fourth-Degree Polynomial Find the...Ch. 3.1 - Height of a Ball If a ball is thrown directly...Ch. 3.1 - Path of a Ball A ball is thrown across a playing...Ch. 3.1 - Revenue A manufacturer finds that the revenue...Ch. 3.1 - Sales A soft-drink vendor at a popular beach...Ch. 3.1 - Advertising The effectiveness of a television...Ch. 3.1 - Pharmaceuticals When a certain drug is taken...Ch. 3.1 - Agriculture The number of apples produced by each...Ch. 3.1 - Agriculture At a certain vineyard it is found that...Ch. 3.1 - Maxima and Minima Use the formulas of this section...Ch. 3.1 - Maxima and Minima Use the formulas of this section...Ch. 3.1 - Maxima and Minima Use the formulas of this section...Ch. 3.1 - Maxima and Minima Use the formulas of this section...Ch. 3.1 - Fencing a Horse Corral Carol has 2400 ft of...Ch. 3.1 - Making a Rain Gutter A rain gutter is formed by...Ch. 3.1 - Stadium Revenue A baseball team plays in a stadium...Ch. 3.1 - Maximizing Profit A community bird-watching...Ch. 3.1 - Prob. 67E Ch. 3.2 - Only one of the following graphs could be the...Ch. 3.2 - Describe the end behavior of each polynomial. (a)...Ch. 3.2 - If c is a zero of the polynomial P, then (a) P(c)...Ch. 3.2 - Which of the following statements couldnt possibly...Ch. 3.2 - Transformations of Monomials Sketch the graph of...Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - End Behavior A polynomial function is given. (a)...Ch. 3.2 - Graphing Factored Polynomials Sketch the graph of...Ch. 3.2 - Prob. 16E Ch. 3.2 - Prob. 17E Ch. 3.2 - Prob. 18E Ch. 3.2 - Prob. 19E Ch. 3.2 - Prob. 20E Ch. 3.2 - Prob. 21E Ch. 3.2 - Prob. 22E Ch. 3.2 - Prob. 23E Ch. 3.2 - Prob. 24E Ch. 3.2 - Prob. 25E Ch. 3.2 - Prob. 26E Ch. 3.2 - Prob. 27E Ch. 3.2 - Prob. 28E Ch. 3.2 - Prob. 29E Ch. 3.2 - Prob. 30E Ch. 3.2 - Graphing Polynomials Factor the polynomial and use...Ch. 3.2 - Prob. 32E Ch. 3.2 - Prob. 33E Ch. 3.2 - Prob. 34E Ch. 3.2 - Prob. 35E Ch. 3.2 - Prob. 36E Ch. 3.2 - Prob. 37E Ch. 3.2 - Prob. 38E Ch. 3.2 - Prob. 39E Ch. 3.2 - Prob. 40E Ch. 3.2 - Prob. 41E Ch. 3.2 - Prob. 42E Ch. 3.2 - Prob. 43E Ch. 3.2 - Prob. 44E Ch. 3.2 - Prob. 45E Ch. 3.2 - Prob. 46E Ch. 3.2 - End Behavior Determine the end behavior of P....Ch. 3.2 - End Behavior Determine the end behavior of P....Ch. 3.2 - Prob. 49E Ch. 3.2 - End Behavior Determine the end behavior of P....Ch. 3.2 - Prob. 51E Ch. 3.2 - Prob. 52E Ch. 3.2 - Prob. 53E Ch. 3.2 - Local Extrema The graph of a polynomial function...Ch. 3.2 - Prob. 55E Ch. 3.2 - Local Extrema Graph the polynomial in the given...Ch. 3.2 - Prob. 57E Ch. 3.2 - Prob. 58E Ch. 3.2 - Prob. 59E Ch. 3.2 - Local Extrema Graph the polynomial in the given...Ch. 3.2 - Prob. 61E Ch. 3.2 - Prob. 62E Ch. 3.2 - Prob. 63E Ch. 3.2 - Prob. 64E Ch. 3.2 - Prob. 65E Ch. 3.2 - Prob. 66E Ch. 3.2 - Prob. 67E Ch. 3.2 - Prob. 68E Ch. 3.2 - Prob. 69E Ch. 3.2 - Prob. 70E Ch. 3.2 - Prob. 71E Ch. 3.2 - Prob. 72E Ch. 3.2 - Prob. 73E Ch. 3.2 - Prob. 74E Ch. 3.2 - Prob. 75E Ch. 3.2 - Families of Polynomials Graph the family of...Ch. 3.2 - Prob. 77E Ch. 3.2 - Prob. 78E Ch. 3.2 - Prob. 79E Ch. 3.2 - Power Functions Portions of the graphs of y = x2,...Ch. 3.2 - Prob. 81E Ch. 3.2 - Prob. 82E Ch. 3.2 - Prob. 83E Ch. 3.2 - Local Extrema These exercises involve local maxima...Ch. 3.2 - Local Extrema These exercises involve local maxima...Ch. 3.2 - Prob. 86E Ch. 3.2 - Market Research A market analyst working for a...Ch. 3.2 - Population Change The rabbit population on a small...Ch. 3.2 - Volume of a Box An open box is to be constructed...Ch. 3.2 - Volume of a Box A cardboard box has a square base,...Ch. 3.2 - Prob. 91E Ch. 3.2 - DISCUSS DISCOVER: Possible Number of Local...Ch. 3.3 - If we divide the polynomial P by the factor x c...Ch. 3.3 - (a) If we divide the polynomial P(x) by the factor...Ch. 3.3 - Division of Polynomials Two polynomials P and D...Ch. 3.3 - Division of Polynomials Two polynomials P and D...Ch. 3.3 - Division of Polynomials Two polynomials P and D...Ch. 3.3 - Division of Polynomials Two polynomials P and D...Ch. 3.3 - Division of Polynomials Two polynomials P and D...Ch. 3.3 - Prob. 8E Ch. 3.3 - Prob. 9E Ch. 3.3 - Prob. 10E Ch. 3.3 - Prob. 11E Ch. 3.3 - Prob. 12E Ch. 3.3 - Prob. 13E Ch. 3.3 - Prob. 14E Ch. 3.3 - Prob. 15E Ch. 3.3 - Prob. 16E Ch. 3.3 - Prob. 17E Ch. 3.3 - Prob. 18E Ch. 3.3 - Prob. 19E Ch. 3.3 - Prob. 20E Ch. 3.3 - Prob. 21E Ch. 3.3 - Prob. 22E Ch. 3.3 - Prob. 23E Ch. 3.3 - Prob. 24E Ch. 3.3 - Prob. 25E Ch. 3.3 - Prob. 26E Ch. 3.3 - Prob. 27E Ch. 3.3 - Prob. 28E Ch. 3.3 - Prob. 29E Ch. 3.3 - Prob. 30E Ch. 3.3 - Prob. 31E Ch. 3.3 - Prob. 32E Ch. 3.3 - Prob. 33E Ch. 3.3 - Prob. 34E Ch. 3.3 - Prob. 35E Ch. 3.3 - Prob. 36E Ch. 3.3 - Prob. 37E Ch. 3.3 - Prob. 38E Ch. 3.3 - Prob. 39E Ch. 3.3 - Prob. 40E Ch. 3.3 - Prob. 41E Ch. 3.3 - Prob. 42E Ch. 3.3 - Prob. 43E Ch. 3.3 - Prob. 44E Ch. 3.3 - Prob. 45E Ch. 3.3 - Prob. 46E Ch. 3.3 - Prob. 47E Ch. 3.3 - Remainder Theorem Use synthetic division and the...Ch. 3.3 - Prob. 49E Ch. 3.3 - Prob. 50E Ch. 3.3 - Prob. 51E Ch. 3.3 - Prob. 52E Ch. 3.3 - Prob. 53E Ch. 3.3 - Factor Theorem Use the Factor Theorem to show that...Ch. 3.3 - Factor Theorem Use the Factor Theorem to show that...Ch. 3.3 - Prob. 56E Ch. 3.3 - Prob. 57E Ch. 3.3 - Prob. 58E Ch. 3.3 - Prob. 59E Ch. 3.3 - Prob. 60E Ch. 3.3 - Factor Theorem Show that the given value(s) of c...Ch. 3.3 - Prob. 62E Ch. 3.3 - Finding a Polynomial with Specified Zeros Find a...Ch. 3.3 - Finding a Polynomial with Specified Zeros Find a...Ch. 3.3 - Finding a Polynomial with Specified Zeros Find a...Ch. 3.3 - Prob. 66E Ch. 3.3 - Polynomials with Specified Zeros Find a polynomial...Ch. 3.3 - Polynomials with Specified Zeros Find a polynomial...Ch. 3.3 - Polynomials with Specified Zeros Find a polynomial...Ch. 3.3 - Prob. 70E Ch. 3.3 - Finding a Polynomial from a Graph Find the...Ch. 3.3 - Finding a Polynomial from a Graph Find the...Ch. 3.3 - Finding a Polynomial from a Graph Find the...Ch. 3.3 - Prob. 74E Ch. 3.3 - DISCUSS: Impossible Division? Suppose you were...Ch. 3.3 - Prob. 76E Ch. 3.4 - If the polynomial function...Ch. 3.4 - Using Descartes Rule of Signs, we can tell that...Ch. 3.4 - True or False? If c is a real zero of the...Ch. 3.4 - True or False? If a is an upper bound for the real...Ch. 3.4 - Prob. 5E Ch. 3.4 - Prob. 6E Ch. 3.4 - Possible Rational Zeros List all possible rational...Ch. 3.4 - Prob. 8E Ch. 3.4 - Prob. 9E Ch. 3.4 - Prob. 10E Ch. 3.4 - Prob. 11E Ch. 3.4 - Prob. 12E Ch. 3.4 - Possible Rational Zeros A polynomial function P...Ch. 3.4 - Possible Rational Zeros A polynomial function P...Ch. 3.4 - Prob. 15E Ch. 3.4 - Integer Zeros All the real zeros of the given...Ch. 3.4 - Prob. 17E Ch. 3.4 - Prob. 18E Ch. 3.4 - Prob. 19E Ch. 3.4 - Integer Zeros All the real zeros of the given...Ch. 3.4 - Prob. 21E Ch. 3.4 - Prob. 22E Ch. 3.4 - Prob. 23E Ch. 3.4 - Prob. 24E Ch. 3.4 - Prob. 25E Ch. 3.4 - Prob. 26E Ch. 3.4 - Prob. 27E Ch. 3.4 - Prob. 28E Ch. 3.4 - Prob. 29E Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Prob. 35E Ch. 3.4 - Prob. 36E Ch. 3.4 - Prob. 37E Ch. 3.4 - Prob. 38E Ch. 3.4 - Prob. 39E Ch. 3.4 - Prob. 40E Ch. 3.4 - Prob. 41E Ch. 3.4 - Prob. 42E Ch. 3.4 - Prob. 43E Ch. 3.4 - Prob. 44E Ch. 3.4 - Prob. 45E Ch. 3.4 - Prob. 46E Ch. 3.4 - Real Zeros of a Polynomial Find all the real zeros...Ch. 3.4 - Real Zeros of a Polynomial Find all the real zeros...Ch. 3.4 - Prob. 49E Ch. 3.4 - Prob. 50E Ch. 3.4 - Prob. 51E Ch. 3.4 - Prob. 52E Ch. 3.4 - Prob. 53E Ch. 3.4 - Prob. 54E Ch. 3.4 - Prob. 55E Ch. 3.4 - Prob. 56E Ch. 3.4 - Prob. 57E Ch. 3.4 - Prob. 58E Ch. 3.4 - Prob. 59E Ch. 3.4 - Prob. 60E Ch. 3.4 - Prob. 61E Ch. 3.4 - Prob. 62E Ch. 3.4 - Descartes Rule of Signs Use Descartes Rule of...Ch. 3.4 - Descartes Rule of Signs Use Descartes Rule of...Ch. 3.4 - Prob. 65E Ch. 3.4 - Prob. 66E Ch. 3.4 - Prob. 67E Ch. 3.4 - Prob. 68E Ch. 3.4 - Prob. 69E Ch. 3.4 - Prob. 70E Ch. 3.4 - Prob. 71E Ch. 3.4 - Prob. 72E Ch. 3.4 - Prob. 73E Ch. 3.4 - Prob. 74E Ch. 3.4 - Prob. 75E Ch. 3.4 - Prob. 76E Ch. 3.4 - Upper and Lower Bounds Find integers that are...Ch. 3.4 - Prob. 78E Ch. 3.4 - Prob. 79E Ch. 3.4 - Prob. 80E Ch. 3.4 - Prob. 81E Ch. 3.4 - Prob. 82E Ch. 3.4 - Prob. 83E Ch. 3.4 - Prob. 84E Ch. 3.4 - Prob. 85E Ch. 3.4 - Prob. 86E Ch. 3.4 - Prob. 87E Ch. 3.4 - Prob. 88E Ch. 3.4 - Prob. 89E Ch. 3.4 - Polynomials With No Rational Zeros Show that the...Ch. 3.4 - Prob. 91E Ch. 3.4 - Prob. 92E Ch. 3.4 - Prob. 93E Ch. 3.4 - Prob. 94E Ch. 3.4 - Prob. 95E Ch. 3.4 - Prob. 96E Ch. 3.4 - Prob. 97E Ch. 3.4 - Prob. 98E Ch. 3.4 - Volume of a Silo A grain silo consists of a...Ch. 3.4 - Dimensions of a Lot A rectangular parcel of land...Ch. 3.4 - Depth of Snowfall Snow began falling at noon on...Ch. 3.4 - Volume of a Box An open box with a volume of 1500...Ch. 3.4 - Volume of a Rocket A rocket consists of a right...Ch. 3.4 - Volume of a Box A rectangular box with a volume of...Ch. 3.4 - Girth of a Box A box with a square base has length...Ch. 3.4 - DISCUSS DISCOVER: How Many Real Zeros Can a...Ch. 3.4 - Prob. 107E Ch. 3.4 - Prob. 108E Ch. 3.4 - PROVE: Upper and Lower Bounds Theorem Let P(x) be...Ch. 3.4 - Prob. 110E Ch. 3.5 - The polynomial P(x) = 5x2(x 4)3(x + 7) has degree...Ch. 3.5 - (a) If a is a zero of the polynomial P, then...Ch. 3.5 - A polynomial of degree n 1 has exactly ________...Ch. 3.5 - If the polynomial function P has real coefficients...Ch. 3.5 - True or False? If False, give a reason. 5. Let...Ch. 3.5 - True or False? If False, give a reason. 6. Let...Ch. 3.5 - Complete Factorization A polynomial P is given....Ch. 3.5 - Prob. 8E Ch. 3.5 - Prob. 9E Ch. 3.5 - Prob. 10E Ch. 3.5 - Prob. 11E Ch. 3.5 - Prob. 12E Ch. 3.5 - Prob. 13E Ch. 3.5 - Prob. 14E Ch. 3.5 - Prob. 15E Ch. 3.5 - Prob. 16E Ch. 3.5 - Prob. 17E Ch. 3.5 - Prob. 18E Ch. 3.5 - Prob. 19E Ch. 3.5 - Prob. 20E Ch. 3.5 - Prob. 21E Ch. 3.5 - Prob. 22E Ch. 3.5 - Prob. 23E Ch. 3.5 - Prob. 24E Ch. 3.5 - Prob. 25E Ch. 3.5 - Prob. 26E Ch. 3.5 - Prob. 27E Ch. 3.5 - Prob. 28E Ch. 3.5 - Prob. 29E Ch. 3.5 - Prob. 30E Ch. 3.5 - Prob. 31E Ch. 3.5 - Prob. 32E Ch. 3.5 - Prob. 33E Ch. 3.5 - Prob. 34E Ch. 3.5 - Prob. 35E Ch. 3.5 - Complete Factorization Factor the polynomial...Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - Prob. 40E Ch. 3.5 - Prob. 41E Ch. 3.5 - Finding a Polynomial with Specified Zeros Find a...Ch. 3.5 - Finding a Polynomial with Specified Zeros Find a...Ch. 3.5 - Prob. 44E Ch. 3.5 - Prob. 45E Ch. 3.5 - Prob. 46E Ch. 3.5 - Prob. 47E Ch. 3.5 - Prob. 48E Ch. 3.5 - Prob. 49E Ch. 3.5 - Prob. 50E Ch. 3.5 - Prob. 51E Ch. 3.5 - Prob. 52E Ch. 3.5 - Prob. 53E Ch. 3.5 - Prob. 54E Ch. 3.5 - Prob. 55E Ch. 3.5 - Prob. 56E Ch. 3.5 - Prob. 57E Ch. 3.5 - Prob. 58E Ch. 3.5 - Prob. 59E Ch. 3.5 - Prob. 60E Ch. 3.5 - Prob. 61E Ch. 3.5 - Finding Complex Zeros Find all zeros of the...Ch. 3.5 - Finding Complex Zeros Find all zeros of the...Ch. 3.5 - Prob. 64E Ch. 3.5 - Prob. 65E Ch. 3.5 - Prob. 66E Ch. 3.5 - Prob. 67E Ch. 3.5 - Prob. 68E Ch. 3.5 - Prob. 69E Ch. 3.5 - Prob. 70E Ch. 3.5 - Prob. 71E Ch. 3.5 - Prob. 72E Ch. 3.5 - (a) Show that 2i and 1 i are both solutions of...Ch. 3.5 - (a) Find the polynomial with real coefficients of...Ch. 3.5 - DISCUSS: Polynomials of Odd Degree The Conjugate...Ch. 3.5 - Prob. 76E Ch. 3.6 - If the rational function y = r(x) has the vertical...Ch. 3.6 - If the rational function y = r(x) has the...Ch. 3.6 - Prob. 3E Ch. 3.6 - Prob. 4E Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - True or False? 8. The graph of a rational function...Ch. 3.6 - Prob. 9E Ch. 3.6 - Table of Values A rational function is given. (a)...Ch. 3.6 - Prob. 11E Ch. 3.6 - Prob. 12E Ch. 3.6 - Graphing Rational Functions Using Transformations...Ch. 3.6 - Prob. 14E Ch. 3.6 - Graphing Rational Functions Using Transformations...Ch. 3.6 - Prob. 16E Ch. 3.6 - Prob. 17E Ch. 3.6 - Prob. 18E Ch. 3.6 - Prob. 19E Ch. 3.6 - Prob. 20E Ch. 3.6 - Prob. 21E Ch. 3.6 - Prob. 22E Ch. 3.6 - Prob. 23E Ch. 3.6 - Prob. 24E Ch. 3.6 - Prob. 25E Ch. 3.6 - Prob. 26E Ch. 3.6 - Prob. 27E Ch. 3.6 - Prob. 28E Ch. 3.6 - Getting Information from a Graph From the graph,...Ch. 3.6 - Prob. 30E Ch. 3.6 - Prob. 31E Ch. 3.6 - Prob. 32E Ch. 3.6 - Prob. 33E Ch. 3.6 - Prob. 34E Ch. 3.6 - Prob. 35E Ch. 3.6 - Prob. 36E Ch. 3.6 - Prob. 37E Ch. 3.6 - Prob. 38E Ch. 3.6 - Prob. 39E Ch. 3.6 - Prob. 40E Ch. 3.6 - Prob. 41E Ch. 3.6 - Prob. 42E Ch. 3.6 - Prob. 43E Ch. 3.6 - Prob. 44E Ch. 3.6 - Prob. 45E Ch. 3.6 - Prob. 46E Ch. 3.6 - Prob. 47E Ch. 3.6 - Prob. 48E Ch. 3.6 - Prob. 49E Ch. 3.6 - Prob. 50E Ch. 3.6 - Graphing Rational Functions Find the intercepts...Ch. 3.6 - Prob. 52E Ch. 3.6 - Prob. 53E Ch. 3.6 - Graphing Rational Functions Find the intercepts...Ch. 3.6 - Prob. 55E Ch. 3.6 - Prob. 56E Ch. 3.6 - Prob. 57E Ch. 3.6 - Prob. 58E Ch. 3.6 - Prob. 59E Ch. 3.6 - Prob. 60E Ch. 3.6 - Prob. 61E Ch. 3.6 - Prob. 62E Ch. 3.6 - Prob. 63E Ch. 3.6 - Prob. 64E Ch. 3.6 - Prob. 65E Ch. 3.6 - Prob. 66E Ch. 3.6 - Prob. 67E Ch. 3.6 - Prob. 68E Ch. 3.6 - Prob. 69E Ch. 3.6 - Prob. 70E Ch. 3.6 - Prob. 71E Ch. 3.6 - Prob. 72E Ch. 3.6 - Prob. 73E Ch. 3.6 - Prob. 74E Ch. 3.6 - Prob. 75E Ch. 3.6 - Prob. 76E Ch. 3.6 - Prob. 77E Ch. 3.6 - Prob. 78E Ch. 3.6 - Prob. 79E Ch. 3.6 - End Behavior Graph the rational function f, and...Ch. 3.6 - Prob. 81E Ch. 3.6 - Prob. 82E Ch. 3.6 - End Behavior Graph the rational function, and find...Ch. 3.6 - End Behavior Graph the rational function, and find...Ch. 3.6 - Prob. 85E Ch. 3.6 - Prob. 86E Ch. 3.6 - Population Growth Suppose that the rabbit...Ch. 3.6 - Drug Concentration After a certain drug is...Ch. 3.6 - Drug Concentration A drug is administered to a...Ch. 3.6 - Flight of a Rocket Suppose a rocket is fired...Ch. 3.6 - The Doppler Effect As a train moves toward an...Ch. 3.6 - Focusing Distance For a camera with a lens of...Ch. 3.6 - Prob. 93E Ch. 3.6 - Prob. 94E Ch. 3.6 - DISCOVER: Transformations of y = 1/x2 In Example 2...Ch. 3.7 - To solve a polynomial inequality, we factor the...Ch. 3.7 - To solve a rational inequality, we factor the...Ch. 3.7 - Prob. 3E Ch. 3.7 - Prob. 4E Ch. 3.7 - Polynomial Inequalities Solve the inequality. 5....Ch. 3.7 - Prob. 6E Ch. 3.7 - Prob. 7E Ch. 3.7 - Prob. 8E Ch. 3.7 - Polynomial Inequalities Solve the inequality. 9....Ch. 3.7 - Prob. 10E Ch. 3.7 - Polynomial Inequalities Solve the inequality. 11....Ch. 3.7 - Prob. 12E Ch. 3.7 - Polynomial Inequalities Solve the inequality. 13....Ch. 3.7 - Prob. 14E Ch. 3.7 - Prob. 15E Ch. 3.7 - Prob. 16E Ch. 3.7 - Prob. 17E Ch. 3.7 - Prob. 18E Ch. 3.7 - Rational Inequalities Solve the inequality. 19....Ch. 3.7 - Prob. 20E Ch. 3.7 - Prob. 21E Ch. 3.7 - Prob. 22E Ch. 3.7 - Prob. 23E Ch. 3.7 - Prob. 24E Ch. 3.7 - Prob. 25E Ch. 3.7 - Prob. 26E Ch. 3.7 - Prob. 27E Ch. 3.7 - Rational Inequalities Solve the inequality. 28....Ch. 3.7 - Prob. 29E Ch. 3.7 - Prob. 30E Ch. 3.7 - Rational Inequalities Solve the inequality. 31....Ch. 3.7 - Prob. 32E Ch. 3.7 - Rational Inequalities Solve the inequality. 33....Ch. 3.7 - Prob. 34E Ch. 3.7 - Prob. 35E Ch. 3.7 - Prob. 36E Ch. 3.7 - Prob. 37E Ch. 3.7 - Prob. 38E Ch. 3.7 - Graphs of Two Functions Find all values of x for...Ch. 3.7 - Prob. 40E Ch. 3.7 - Domain of a Function Find the domain of the given...Ch. 3.7 - Prob. 42E Ch. 3.7 - Domain of a Function Find the domain of the given...Ch. 3.7 - Prob. 44E Ch. 3.7 - Prob. 45E Ch. 3.7 - Prob. 46E Ch. 3.7 - Prob. 47E Ch. 3.7 - Prob. 48E Ch. 3.7 - Prob. 49E Ch. 3.7 - Prob. 50E Ch. 3.7 - Prob. 51E Ch. 3.7 - Prob. 52E Ch. 3.7 - Prob. 53E Ch. 3.7 - Prob. 54E Ch. 3.7 - Bonfire Temperature In the vicinity of a bonfire...Ch. 3.7 - Stopping Distance For a certain model of car the...Ch. 3.7 - Managing Traffic A highway engineer develops a...Ch. 3.7 - Prob. 58E Ch. 3 - (a) What is the degree of a quadratic function f?...Ch. 3 - Prob. 2RCC Ch. 3 - Prob. 3RCC Ch. 3 - Prob. 4RCC Ch. 3 - Prob. 5RCC Ch. 3 - Prob. 6RCC Ch. 3 - Prob. 7RCC Ch. 3 - Prob. 8RCC Ch. 3 - Prob. 9RCC Ch. 3 - Prob. 10RCC Ch. 3 - Prob. 11RCC Ch. 3 - Prob. 12RCC Ch. 3 - Prob. 13RCC Ch. 3 - Prob. 14RCC Ch. 3 - Prob. 1RE Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Profit The profit P (in dollars) generated by...Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 23RE Ch. 3 - Prob. 24RE Ch. 3 - Strength of a Beam The strength S of a wooden beam...Ch. 3 - Volume A small shelter for delicate plants is to...Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Number of Possible Zeros A polynomial P is given....Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 48RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE Ch. 3 - Prob. 74RE Ch. 3 - Prob. 75RE Ch. 3 - Prob. 76RE Ch. 3 - Prob. 77RE Ch. 3 - Prob. 78RE Ch. 3 - Prob. 79RE Ch. 3 - Prob. 80RE Ch. 3 - Prob. 81RE Ch. 3 - Graphing Rational Functions Graph the rational...Ch. 3 - Prob. 83RE Ch. 3 - Prob. 84RE Ch. 3 - Prob. 85RE Ch. 3 - Prob. 86RE Ch. 3 - Prob. 87RE Ch. 3 - Prob. 88RE Ch. 3 - Prob. 89RE Ch. 3 - Prob. 90RE Ch. 3 - Prob. 91RE Ch. 3 - Prob. 92RE Ch. 3 - Prob. 93RE Ch. 3 - Prob. 94RE Ch. 3 - Prob. 95RE Ch. 3 - Polynomial Inequalities Solve the inequality. 96....Ch. 3 - Prob. 97RE Ch. 3 - Prob. 98RE Ch. 3 - Prob. 99RE Ch. 3 - Prob. 100RE Ch. 3 - Prob. 101RE Ch. 3 - Prob. 102RE Ch. 3 - Prob. 103RE Ch. 3 - Prob. 104RE Ch. 3 - Prob. 105RE Ch. 3 - Prob. 106RE Ch. 3 - Express the quadratic function f(x) = x2 x 6 in...Ch. 3 - Find the maximum or minimum value of the quadratic...Ch. 3 - A cannonball fired out to sea from a shore battery...Ch. 3 - Graph the polynomial P(x) = (x + 2)3 + 27, showing...Ch. 3 - (a) Use synthetic division to find the quotient...Ch. 3 - Let P(x) = 2x3 5x2 4x + 3. (a) List all possible...Ch. 3 - Find all real and complex zeros of P(x) = x3 x2 ...Ch. 3 - Find the complete factorization of P(x) = x4 2x3...Ch. 3 - Find a fourth-degree polynomial with integer...Ch. 3 - Let P(x) = 2x4 7x3 + x2 18x + 3. (a) Use...Ch. 3 - Consider the following rational functions:...Ch. 3 - Prob. 12T Ch. 3 - Prob. 13T Ch. 3 - Prob. 14T Ch. 3 - Tire Inflation and Treadwear Car tires need to be...Ch. 3 - Too Many Corn Plants per Acre? The more corn a...Ch. 3 - How Fast Can You List Your Favorite Things? If you...Ch. 3 - Height of a Baseball A baseball is thrown upward,...Ch. 3 - Torricelli's Law Water in a tank will flow out of...

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 possible zeros of the polynomial P ( x ) = 8 x 5 − 14 x 4 − 22 x 3 + 57 x 2 − 35 x + 6 .

Solution Summary: The author explains the rational zeros theorem for the polynomial P(x)=a_nx

Concept explainers

Videos

The possible zeros of the polynomial P(x)=8x5−14x4−22x3+57x2−35x+6 .

Want to see the full answer?

Chapter 3 Solutions