Explanation Given: The equation is x 3 − 4 x 2 + x + 6 . Calculation: Perform the synthetic division of x 3 − 4 x 2 + x + 6 by ( x + 1 ) as follows: The synthetic division of a polynomial a n x n + a n − 1 x n − 1 + a n − 2 x n − 2 + … + a 1 + a 0 by the binomial of the form x − c is started off by writing the coefficients in the following format: c a n a n − 1 ⋯ a 1 a 0 For the example provided, this would turn to, − 1 | 1 − 4 1 6 Now proceed with the synthetic division: − 1 | 1 − 4 1 6 − 1 5 − 6 1 − 5 6 0 Now, the first 3 entries in the last row represent the coefficients of a polynomial with degree one less than the dividend and the last entry represents the remainder. So, the quotient, which would have degree 3, can now be written as degree 2, x 2 − 5 x + 6 The remainder is 0 . The remainder theorem states that when f ( x ) is divided by x − a . f ( x ) = g ( x ) ( x − a ) + r ( x ) The remainder theorem states that when f ( x ) is divided by x − a

Intermediate Algebra for College Students (7th Edition)

7th Edition

ISBN: 9780134178943

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 6.5, Problem 27E

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To calculate: All the roots of x3−4x2+x+6 by using synthetic division with the

divisor x+1.

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Chapter 6.5, Problem 26E

Chapter 6.5, Problem 28E

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Chapter 6 Solutions

Intermediate Algebra for College Students (7th Edition)

Ch. 6.1 - Check Point 1 Use the rational function in...Ch. 6.1 - Check Point 2 Find the domain of f if...Ch. 6.1 - Prob. 3CP Ch. 6.1 - Prob. 4CP Ch. 6.1 - Prob. 5CP Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 7CP Ch. 6.1 - Prob. 1CVC Ch. 6.1 - Prob. 2CVC Ch. 6.1 - Prob. 3CVC

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All the roots of x 3 − 4 x 2 + x + 6 by using synthetic division with the divisor x + 1 .

Solution Summary: The author explains how to calculate all the roots of x3-4+x+6 by using synthetic division with the divisor x+1.

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To calculate: All the roots of x3−4x2+x+6 by using synthetic division with the

divisor x+1.

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Chapter 6 Solutions

All the roots of x 3 − 4 x 2 + x + 6 by using synthetic division with the divisor x + 1 .

Solution Summary: The author explains how to calculate all the roots of x3-4+x+6 by using synthetic division with the divisor x+1.

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To calculate: All the roots of x3−4x2+x+6 by using synthetic division with the divisor x+1.

Want to see the full answer?

Chapter 6 Solutions

To calculate: All the roots of x3−4x2+x+6 by using synthetic division with the

divisor x+1.