Explanation Given: The solution of polynomial x 3 + 4 x 2 − x − 4 = 0 is x = 1 . Procedure used: Synthetic division method: “To divide a polynomial by ( x − a ) : 1. Arrange the coefficients in descending powers of x , with a 0 for any missing power. Place a from ( x − a ) to the left of the coefficients. 2. Bring down the first coefficient to the third line. Multiply the last number in the third line by a and write the product in the second line under the next term. 3. Add the last number in the second line to the number above it in the first line. Continue this process until all numbers in the first line are used. 4. The third line represents the coefficients of the quotient, with the last number the remainder. The quotient is a polynomial of degree one less than the dividend. If the remainder is 0, x − a is a factor of the polynomial, and the polynomial can be written as the product of the divisor x − a and the quotient.” Calculation: Consider the polynomial p ( x ) = x 3 + 4 x 2 − x − 4 . If the solution of the polynomial is 1 , then x − 1 is a factor of the polynomial. Obtain the factor polynomial other than x − 1 . Divide the polynomial p ( x ) = x 3 + 4 x 2 − x − 4 by x − 1 . Use step 1 and set the coefficients in descending powers of x . 1 4 − 1 − 4 Set 1 from x − 1 to the left of the coefficients. 1 1 4 − 1 − 4 Use step 2 and 3 mentioned in Synthetic division method and bring 1 to the last entry (that is, last from the right end) of third line and multiply 1 by a , which is 1 and write the product 1 in second line under next term and add the number 1 in the second line and the number above it, that is, 4 in first line

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Chapter 6.4, Problem 10E

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To find: The remaining solutions to the polynomial equation x3+4x2−x−4=0 by using the synthetic division.

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Chapter 6.4, Problem 9E

Chapter 6.4, Problem 11E

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Chapter 6 Solutions

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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. 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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 - 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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. 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The remaining solutions to the polynomial equation x 3 + 4 x 2 − x − 4 = 0 by using the synthetic division.

Solution Summary: The author explains how to find the remaining solutions to the polynomial equation by using the synthetic division method.

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To find: The remaining solutions to the polynomial equation x3+4x2−x−4=0 by using the synthetic division.

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Chapter 6 Solutions