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

See similar textbooks

Videos

Question

Chapter 6.5, Problem 27E

To determine

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

divisor x+1.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6.5, Problem 26E

Chapter 6.5, Problem 28E

Students have asked these similar questions

In Exercises 133–136, factor each polynomial completely. Assume that any variable exponents represent whole numbers. 133. y + x + x + y 134. 36x2" – y2n 135. x* 3n 12n 136. 4x2" + 20x"y" + 25y2m

In Exercises 132–137, factor each polynomial. Assume that all variable exponents represent whole numbers. 132. 9x2" + x" – 8 133. 4x2n – 9x" + 5 134. an+2 – a"+2 – 6a? 135. b2n+2 + 3b"+2 10b2 136. 3c"+2 10c"+1 + 3c" 137. 2d"+2 5d"+1 + 3d"

Write the exact equation of a polynomial whose graph contains the points (1, 0), (–5, 0), (–2, 0), and (–4, 30).Remember to solve for a!

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

Knowledge Booster

$Algebra$

Learn more about

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

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.

Videos

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

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.

Videos

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.