Explanation Given: The polynomial is, P ( x ) = x 4 − 6 x 3 + x − 2 and the divisor is d ( x ) = x − 1 . 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 coefficient 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 P ( x ) = x 4 − 6 x 3 + x − 2 by d ( x ) = x − 1 . Write 0 as coefficient for missing terms x 2 , the given polynomial x 4 − 6 x 3 + x − 2 becomes x 4 − 6 x 3 + 0 x 2 + x − 2 . Use the above procedure to find the quotient of the given expression. x − 1 x 3 − 5 x 2 − 5 x − 4 x 4 − 6 x 3 + 0 x 2 + x − 2 x 4 − x 3 _ − 5 x 3 + 0 x 2 − 5 x 3 + 5 x 2 _ − 5 x 2 + x − 5 x 2 + 5 x _ − 4 x − 2

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, Problem 15MC

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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 express P(x) in the form d(x)⋅Q(x)+R(x).

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Chapter 4, Problem 14MC

Chapter 4, Problem 16MC

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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 express P ( x ) in the form d ( x ) ⋅ Q ( x ) + R ( x ) .

Solution Summary: The author calculates the quotient Q(x) and the remainder R left (x-), using the long division method.

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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 express P(x) in the form d(x)⋅Q(x)+R(x).

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Chapter 4 Solutions