Angel and Barbara were both asked to factor the following polynomial completely. Is one of them correct? Both of them? Neither of them? Explain what each of them did that was correct and/or incorrect. Angel 6x²+20x-16 2(3x²+10x-8) 2( 3x-2)(x+4) Barbara 6x²+20x-16 (6x-4)(x+4)
Angel and Barbara were both asked to factor the following polynomial completely. Is one of them correct? Both of them? Neither of them? Explain what each of them did that was correct and/or incorrect. Angel 6x²+20x-16 2(3x²+10x-8) 2( 3x-2)(x+4) Barbara 6x²+20x-16 (6x-4)(x+4)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![### Factoring Polynomials: A Comparison of Two Approaches
#### Problem Statement
Angel and Barbara were both asked to factor the following polynomial completely:
\[ 6x^2 + 20x - 16 \]
Is one of them correct? Both of them? Neither of them? Explain what each of them did that was correct and/or incorrect.
---
#### Angel's Approach
1. **Initial Polynomial:**
\[ 6x^2 + 20x - 16 \]
2. **First Step:**
\[ 2(3x^2 + 10x - 8) \]
3. **Second Step:**
\[ 2 (3x - 2)(x + 4) \]
---
#### Barbara's Approach
1. **Initial Polynomial:**
\[ 6x^2 + 20x - 16 \]
2. **First and Final Step:**
\[ (6x - 4)(x + 4) \]
---
### Analysis and Explanation
#### Angel's Work
Angel started by factoring out a common factor of 2 from the polynomial:
\[ 6x^2 + 20x - 16 \rightarrow 2(3x^2 + 10x - 8) \]
Then, Angel factored the remaining quadratic expression:
\[ 2(3x^2 + 10x - 8) \rightarrow 2(3x - 2)(x + 4) \]
#### Barbara's Work
Barbara directly factored the polynomial as follows:
\[ 6x^2 + 20x - 16 \rightarrow (6x - 4)(x + 4) \]
### Verification of Factoring
To determine if the factored forms are correct, we can expand the expressions and see if they match the original polynomial.
1. **Angel's Factoring:**
\[ 2(3x - 2)(x + 4) \]
Expanding the terms inside the parentheses first:
\[ (3x - 2)(x + 4) = 3x^2 + 12x - 2x - 8 = 3x^2 + 10x - 8 \]
Now, multiplying by 2:
\[ 2(3x^2 + 10x - 8) = 6x^2 + 20x - 16 \]
Angel's fact](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c5ae3a2-e137-4f19-a2f9-517c9eb84a5f%2F9e00683d-0738-49d8-9e34-dfb229646dcc%2Fe35utik.jpeg&w=3840&q=75)
Transcribed Image Text:### Factoring Polynomials: A Comparison of Two Approaches
#### Problem Statement
Angel and Barbara were both asked to factor the following polynomial completely:
\[ 6x^2 + 20x - 16 \]
Is one of them correct? Both of them? Neither of them? Explain what each of them did that was correct and/or incorrect.
---
#### Angel's Approach
1. **Initial Polynomial:**
\[ 6x^2 + 20x - 16 \]
2. **First Step:**
\[ 2(3x^2 + 10x - 8) \]
3. **Second Step:**
\[ 2 (3x - 2)(x + 4) \]
---
#### Barbara's Approach
1. **Initial Polynomial:**
\[ 6x^2 + 20x - 16 \]
2. **First and Final Step:**
\[ (6x - 4)(x + 4) \]
---
### Analysis and Explanation
#### Angel's Work
Angel started by factoring out a common factor of 2 from the polynomial:
\[ 6x^2 + 20x - 16 \rightarrow 2(3x^2 + 10x - 8) \]
Then, Angel factored the remaining quadratic expression:
\[ 2(3x^2 + 10x - 8) \rightarrow 2(3x - 2)(x + 4) \]
#### Barbara's Work
Barbara directly factored the polynomial as follows:
\[ 6x^2 + 20x - 16 \rightarrow (6x - 4)(x + 4) \]
### Verification of Factoring
To determine if the factored forms are correct, we can expand the expressions and see if they match the original polynomial.
1. **Angel's Factoring:**
\[ 2(3x - 2)(x + 4) \]
Expanding the terms inside the parentheses first:
\[ (3x - 2)(x + 4) = 3x^2 + 12x - 2x - 8 = 3x^2 + 10x - 8 \]
Now, multiplying by 2:
\[ 2(3x^2 + 10x - 8) = 6x^2 + 20x - 16 \]
Angel's fact
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 5 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education