Explanation Given Information: The polynomial expression is x 3 + 4 x 2 − 2 x − 8 . Formula used: The distributive property is, a ( b + c ) = a b + a c Commutative property of multiplication is, a b = b a Calculation: Here, the expression, x 3 + 4 x 2 − 2 x − 8 has four terms. It is not in factored form as it is a combination of four different terms. Recall that the following four steps are involved while factoring a polynomial with four terms by grouping. Step 1: The terms are arranged into two groups in such a way that each group has a common factor. Step 2: Factor out the GCD from each group. Step 3: Factor out a common binomial factor, thus obtained. Step 4: If the common binomial factor is not involved, then try by forming new groups in step 1. In view of the above steps, in the given calculations, the first step is correct where the four terms are collected into two groups. The problem occurs when instead of taking − 2 as common from the second group, the number 2 is taken as common from the second group. This gives two dissimilar binomial terms x + 4 and − x − 4 . If instead of the number 2 , the number − 2 is taken out common from the second group

Beginning and Intermediate Algebra (6th Edition)

6th Edition

ISBN: 9780321969163

Author: Margaret L. Lial, John Hornsby, Terry McGinnis

Publisher: PEARSON

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Chapter 5.1, Problem 77E

To determine

To calculate: The factored form of x3+4x2−2x−8 by factoring out the greatest common factor

and also determine what went wrong in the below calculations,

x3+4x2−2x−8=(x3+4x2)+(−2x−8)=x2(x+4)+2(−x−4)

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Chapter 5.1, Problem 76E

Chapter 5.1, Problem 78E

Chapter 5 Solutions

Beginning and Intermediate Algebra (6th Edition)

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The factored form of x 3 + 4 x 2 − 2 x − 8 by factoring out the greatest common factor and also determine what went wrong in the below calculations, x 3 + 4 x 2 − 2 x − 8 = ( x 3 + 4 x 2 ) + ( − 2 x − 8 ) = x 2 ( x + 4 ) + 2 ( − x − 4 )

Solution Summary: The author explains how to calculate the factored form of the polynomial x3+42-2x-8 by factoring out the greatest common factor.

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To calculate: The factored form of x3+4x2−2x−8 by factoring out the greatest common factor

and also determine what went wrong in the below calculations,

x3+4x2−2x−8=(x3+4x2)+(−2x−8)=x2(x+4)+2(−x−4)

Want to see the full answer?

Chapter 5 Solutions

The factored form of x 3 + 4 x 2 − 2 x − 8 by factoring out the greatest common factor and also determine what went wrong in the below calculations, x 3 + 4 x 2 − 2 x − 8 = ( x 3 + 4 x 2 ) + ( − 2 x − 8 ) = x 2 ( x + 4 ) + 2 ( − x − 4 )

Solution Summary: The author explains how to calculate the factored form of the polynomial x3+42-2x-8 by factoring out the greatest common factor.

Videos

To calculate: The factored form of x3+4x2−2x−8 by factoring out the greatest common factor and also determine what went wrong in the below calculations, x3+4x2−2x−8=(x3+4x2)+(−2x−8)=x2(x+4)+2(−x−4)

Want to see the full answer?

Chapter 5 Solutions

To calculate: The factored form of x3+4x2−2x−8 by factoring out the greatest common factor

and also determine what went wrong in the below calculations,

x3+4x2−2x−8=(x3+4x2)+(−2x−8)=x2(x+4)+2(−x−4)