Explanation Procedure used: Synthetic Division: “1. Write the coefficients of f ( x ) . Be certain that the powers are in descending order and that zeros are inserted for missing powers. 2. Carry down the left coefficient, then multiply it by r , and place this product under the second coefficient of the top line. 3. Add the two numbers in the second column and place the result below. Multiply this sum by r and place the product under the third coefficient of the top line. 4. Continue this process until the bottom row has as many numbers as the top row”. The Factor Theorem: “If f ( r ) = 0 , then x = r is a zero of f ( x ) , x − r is a factor of f ( x ) and x = r is a root of the equation f ( x ) = 0 ”. Calculation: Divide the polynomial 2 x 5 − x 3 + 3 x 2 − 4 by x + 1 as follows. The remainder is zero, x + 1 is a factor of 2 x 5 − x 3 + 3 x 2 − 4 . The powers of x are in descending order, write down the coefficient of f ( x ) and zeros are inserted for missing powers, write − 1 for the divisor x + 1 and place − 1 to the right. 2 0 − 1 3 0 − 4 − 1 Carry the left coefficient 2 to the bottom line and multiply it by − 1 , and place the product − 2 under the second coefficient 0 of the top line and proceed in this similar manner to find the remainder. 2 0 − 1 3 0 − 4 − 1 − 2 2

11th Edition

ISBN: 9780134437705

Author: Washington

Publisher: PEARSON

See similar textbooks

Concept explainers

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Videos

Question

Chapter 15.1, Problem 33E

To determine

Whether x+1 is factor of 2x5−x3+3x2−4 or not by using factor theorem and synthetic division.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 15.1, Problem 32E

Chapter 15.1, Problem 34E

Students have asked these similar questions

3. A spring is stretched 6 in. by a mass that weighs 8 lb. The mass is attached to a dashpot mechanism that has a damping constant of 0.25 lb-sec./ft. and is acted on by an external force of 4 cos 2t lb. a. Set-up the differential equation and initial value problem for the system. b. Write the function in phase-amplitude form. C. Determine the transient solution to the system. Show your work. d. Determine the steady state of this system. Show your work. e. Is the system underdamped, overdamped or critically damped? Explain what this means for the system.

4. Suppose that you have a circuit with a resistance of 20, inductance of 14 H and a capacitance of 11 F. An EMF with equation of E(t) = 6 cos 4t supplies a continuous charge 60 to the circuit. Suppose that the q(0)= 8 V and the q'(0)=7. Use this information to answer the following questions a. Find the function that models the charge of this circuit. b. Is the circuit underdamped, overdamped or critically damped?

1. Solve the initial value problem: y" -11y' + 30y = x³e6x y(0) 11, y'(0) = 36 =

Chapter 15 Solutions

Basic Technical Mathematics

Ch. 15.1 - Use the factor theorem to determine whether t − 2...Ch. 15.1 - Prob. 2PE Ch. 15.1 - Prob. 3PE Ch. 15.1 - Prob. 4PE Ch. 15.1 - Prob. 1E Ch. 15.1 - Prob. 2E Ch. 15.1 - In Exercises 1–4, make the given changes in the...Ch. 15.1 - Prob. 4E Ch. 15.1 - Prob. 5E Ch. 15.1 - Prob. 6E

Ch. 15.1 - Prob. 7E Ch. 15.1 - Prob. 8E Ch. 15.1 - Prob. 9E Ch. 15.1 - Prob. 10E Ch. 15.1 - Prob. 11E Ch. 15.1 - Prob. 12E Ch. 15.1 - Prob. 13E Ch. 15.1 - Prob. 14E Ch. 15.1 - Prob. 15E Ch. 15.1 - Prob. 16E Ch. 15.1 - Prob. 17E Ch. 15.1 - Prob. 18E Ch. 15.1 - Prob. 19E Ch. 15.1 - Prob. 20E Ch. 15.1 - Prob. 21E Ch. 15.1 - Prob. 22E Ch. 15.1 - Prob. 23E Ch. 15.1 - Prob. 24E Ch. 15.1 - Prob. 25E Ch. 15.1 - Prob. 26E Ch. 15.1 - Prob. 27E Ch. 15.1 - Prob. 28E Ch. 15.1 - Prob. 29E Ch. 15.1 - Prob. 30E Ch. 15.1 - Prob. 31E Ch. 15.1 - Prob. 32E Ch. 15.1 - Prob. 33E Ch. 15.1 - Prob. 34E Ch. 15.1 - Prob. 35E Ch. 15.1 - Prob. 36E Ch. 15.1 - Prob. 37E Ch. 15.1 - Prob. 38E Ch. 15.1 - Prob. 39E Ch. 15.1 - Prob. 40E Ch. 15.1 - Prob. 41E Ch. 15.1 - Prob. 42E Ch. 15.1 - Prob. 43E Ch. 15.1 - Prob. 44E Ch. 15.1 - Prob. 45E Ch. 15.1 - Prob. 46E Ch. 15.1 - Prob. 47E Ch. 15.1 - Prob. 48E Ch. 15.1 - Prob. 49E Ch. 15.1 - Prob. 50E Ch. 15.1 - Prob. 51E Ch. 15.1 - Prob. 52E Ch. 15.1 - Prob. 53E Ch. 15.1 - Prob. 54E Ch. 15.1 - Prob. 55E Ch. 15.1 - Prob. 56E Ch. 15.1 - Prob. 57E Ch. 15.1 - Prob. 58E Ch. 15.1 - Prob. 59E Ch. 15.1 - Prob. 60E Ch. 15.2 - Prob. 1PE Ch. 15.2 - Prob. 2PE Ch. 15.2 - Prob. 1E Ch. 15.2 - Prob. 2E Ch. 15.2 - Prob. 3E Ch. 15.2 - Prob. 4E Ch. 15.2 - Prob. 5E Ch. 15.2 - Prob. 6E Ch. 15.2 - Prob. 7E Ch. 15.2 - Prob. 8E Ch. 15.2 - Prob. 9E Ch. 15.2 - Prob. 10E Ch. 15.2 - Prob. 11E Ch. 15.2 - Prob. 12E Ch. 15.2 - Prob. 13E Ch. 15.2 - Prob. 14E Ch. 15.2 - Prob. 15E Ch. 15.2 - Prob. 16E Ch. 15.2 - Prob. 17E Ch. 15.2 - Prob. 18E Ch. 15.2 - Prob. 19E Ch. 15.2 - Prob. 20E Ch. 15.2 - Prob. 21E Ch. 15.2 - Prob. 22E Ch. 15.2 - Prob. 23E Ch. 15.2 - Prob. 24E Ch. 15.2 - Prob. 25E Ch. 15.2 - Prob. 26E Ch. 15.2 - Prob. 27E Ch. 15.2 - Prob. 28E Ch. 15.2 - Prob. 29E Ch. 15.2 - Prob. 30E Ch. 15.2 - Prob. 31E Ch. 15.2 - Prob. 32E Ch. 15.3 - Determine the maximum possible number of positive...Ch. 15.3 - Prob. 2PE Ch. 15.3 - In Exercises 1 and 2, make the given changes in...Ch. 15.3 - Prob. 2E Ch. 15.3 - Prob. 3E Ch. 15.3 - Prob. 4E Ch. 15.3 - Prob. 5E Ch. 15.3 - Prob. 6E Ch. 15.3 - Prob. 7E Ch. 15.3 - Prob. 8E Ch. 15.3 - In Exercises 3–20, solve the given equations...Ch. 15.3 - Prob. 10E Ch. 15.3 - Prob. 11E Ch. 15.3 - Prob. 12E Ch. 15.3 - Prob. 13E Ch. 15.3 - Prob. 14E Ch. 15.3 - Prob. 15E Ch. 15.3 - Prob. 16E Ch. 15.3 - Prob. 17E Ch. 15.3 - Prob. 18E Ch. 15.3 - Prob. 19E Ch. 15.3 - Prob. 20E Ch. 15.3 - Prob. 21E Ch. 15.3 - Prob. 22E Ch. 15.3 - Prob. 23E Ch. 15.3 - Prob. 24E Ch. 15.3 - Prob. 25E Ch. 15.3 - Prob. 26E Ch. 15.3 - Prob. 27E Ch. 15.3 - Prob. 28E Ch. 15.3 - Prob. 29E Ch. 15.3 - Prob. 30E Ch. 15.3 - Prob. 31E Ch. 15.3 - Prob. 32E Ch. 15.3 - Prob. 33E Ch. 15.3 - Prob. 34E Ch. 15.3 - Prob. 35E Ch. 15.3 - Prob. 36E Ch. 15.3 - Prob. 37E Ch. 15.3 - Prob. 38E Ch. 15.3 - Prob. 39E Ch. 15.3 - Prob. 40E Ch. 15.3 - Prob. 41E Ch. 15.3 - Prob. 42E Ch. 15.3 - Prob. 43E Ch. 15.3 - Prob. 44E Ch. 15 - Prob. 1RE Ch. 15 - Prob. 2RE Ch. 15 - Prob. 3RE Ch. 15 - Prob. 4RE Ch. 15 - Prob. 5RE Ch. 15 - Prob. 6RE Ch. 15 - Prob. 7RE Ch. 15 - Prob. 8RE Ch. 15 - Prob. 9RE Ch. 15 - Prob. 10RE Ch. 15 - Prob. 11RE Ch. 15 - Prob. 12RE Ch. 15 - Prob. 13RE Ch. 15 - Prob. 14RE Ch. 15 - Prob. 15RE Ch. 15 - Prob. 16RE Ch. 15 - Prob. 17RE Ch. 15 - Prob. 18RE Ch. 15 - Prob. 19RE Ch. 15 - Prob. 20RE Ch. 15 - Prob. 21RE Ch. 15 - Prob. 22RE Ch. 15 - Prob. 23RE Ch. 15 - Prob. 24RE Ch. 15 - Prob. 25RE Ch. 15 - Prob. 26RE Ch. 15 - Prob. 27RE Ch. 15 - Prob. 28RE Ch. 15 - Prob. 29RE Ch. 15 - Prob. 30RE Ch. 15 - Prob. 31RE Ch. 15 - Prob. 32RE Ch. 15 - Prob. 33RE Ch. 15 - Prob. 34RE Ch. 15 - Prob. 35RE Ch. 15 - Prob. 36RE Ch. 15 - Prob. 37RE Ch. 15 - Prob. 38RE Ch. 15 - Prob. 39RE Ch. 15 - Prob. 40RE Ch. 15 - Prob. 41RE Ch. 15 - Prob. 42RE Ch. 15 - Prob. 43RE Ch. 15 - Prob. 44RE Ch. 15 - Prob. 45RE Ch. 15 - Prob. 46RE Ch. 15 - Prob. 47RE Ch. 15 - Prob. 48RE Ch. 15 - Prob. 49RE Ch. 15 - Prob. 50RE Ch. 15 - Prob. 51RE Ch. 15 - Prob. 52RE Ch. 15 - Prob. 54RE Ch. 15 - Prob. 55RE Ch. 15 - Prob. 56RE Ch. 15 - Prob. 57RE Ch. 15 - Prob. 58RE Ch. 15 - Prob. 59RE Ch. 15 - Prob. 60RE Ch. 15 - Prob. 61RE Ch. 15 - Prob. 62RE Ch. 15 - Prob. 63RE Ch. 15 - Prob. 64RE Ch. 15 - Prob. 65RE Ch. 15 - Prob. 66RE Ch. 15 - Prob. 67RE Ch. 15 - Prob. 68RE Ch. 15 - Prob. 69RE Ch. 15 - Prob. 70RE Ch. 15 - Prob. 71RE Ch. 15 - Prob. 1PT Ch. 15 - Prob. 2PT Ch. 15 - Prob. 3PT Ch. 15 - Prob. 4PT Ch. 15 - Prob. 5PT Ch. 15 - Prob. 6PT Ch. 15 - Prob. 7PT Ch. 15 - Prob. 8PT

Knowledge Booster

Learn more about

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

Whether x + 1 is factor of 2 x 5 − x 3 + 3 x 2 − 4 or not by using factor theorem and synthetic division.

Concept explainers

Videos

Whether x+1 is factor of 2x5−x3+3x2−4 or not by using factor theorem and synthetic division.

Want to see the full answer?

Chapter 15 Solutions