Explanation Given: The polynomial is P ( x ) = x 3 − 8 . The divisor is d ( x ) = x + 2 . Procedure used: Long division method: Step 1: Ensure that the polynomial is written in the descending order with respect to its degree and if any terms are missing in the order, add the terms with the co-efficient zero. Step 2: Divide the highest-degree term of the dividend by the highest-degree term of the divisor and align the like terms vertically. Step 3: Multiply the divisor and the answer obtained in the step 2. Step 4: Subtract the product obtained in step 3 from the dividend and bring down the next term. Step 5: Continue the above steps 1 to 4 until there are no terms left to bring down. Calculation: Divide the polynomial x 3 − 8 by x + 2 . Write 0 as coefficient for missing terms x 2 and x , the given polynomial x 3 − 8 becomes x 3 + 0 x 2 + 0 x − 8 . Use the above procedure to find the quotient of the given expression. x + 2 x 2 − 2 x + 4 x 3 + 0 x 2 + 0 x − 8 x 3 + 2 x 2 _ − 2 x 2 + 0 x − 2 x 2 − 4 x _ 4 x − 8 4 x + 8 _

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

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Chapter 4.3, Problem 5E

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To find: The quotient Q(x) and the remainder R(x) by using long division when P(x) is divided by d(x) and then express P(x) in the form d(x)⋅Q(x)+R(x).

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Chapter 4.3, Problem 4E

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Chapter 4 Solutions

College Algebra: Graphs and Models (6th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 10E

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The quotient Q ( x ) and the remainder R ( x ) by using long division when P ( x ) is divided by d ( x ) and then express P ( x ) in the form d ( x ) ⋅ Q ( x ) + R ( x ) .

Solution Summary: The author explains how to find the quotient of the given expression by using long division.

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To find: The quotient Q(x) and the remainder R(x) by using long division when P(x) is divided by d(x) and then express P(x) in the form d(x)⋅Q(x)+R(x).

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Chapter 4 Solutions