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,...
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![**Factoring Polynomials: An Educational Guide**
### Topic: Factoring Polynomials Completely
In this exercise, you are asked to completely factor the polynomial expression. It is important to consider factoring out common terms, and if necessary, include -1 as one of the factors.
#### Given Polynomial Expression:
\[ 2x^3z - 8x^2z + 18xz - 72z \]
#### Task:
Completely factor the given expression.
#### Sample Solution:
The polynomial might be simplified by identifying the greatest common divisor (GCD) of all terms and factoring out common factors. The solution requires recognizing common factors and potentially using techniques such as grouping or the distributive property.
#### Common Mistake:
In the image, an attempt is made, but it results in an incorrect factorization, as indicated by the red "X" mark and an empty textbox:
Please ensure to review all steps in your factorization process thoroughly for accuracy. Revisit concepts such as the distributive property and factoring by grouping to aid in achieving the correct factorization.
Remember:
1. Look for a GCD in all the terms.
2. Factor out the GCD.
3. Use factoring techniques such as grouping if necessary.
Reattempt the problem step by step to ensure you have completely factored the expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1b91f986-cff4-42a8-8faf-14c1255b04a2%2F48d799e3-89c5-4b1a-b787-15bc89ab8fbd%2F5714rkm_processed.png&w=3840&q=75)
Transcribed Image Text:**Factoring Polynomials: An Educational Guide**
### Topic: Factoring Polynomials Completely
In this exercise, you are asked to completely factor the polynomial expression. It is important to consider factoring out common terms, and if necessary, include -1 as one of the factors.
#### Given Polynomial Expression:
\[ 2x^3z - 8x^2z + 18xz - 72z \]
#### Task:
Completely factor the given expression.
#### Sample Solution:
The polynomial might be simplified by identifying the greatest common divisor (GCD) of all terms and factoring out common factors. The solution requires recognizing common factors and potentially using techniques such as grouping or the distributive property.
#### Common Mistake:
In the image, an attempt is made, but it results in an incorrect factorization, as indicated by the red "X" mark and an empty textbox:
Please ensure to review all steps in your factorization process thoroughly for accuracy. Revisit concepts such as the distributive property and factoring by grouping to aid in achieving the correct factorization.
Remember:
1. Look for a GCD in all the terms.
2. Factor out the GCD.
3. Use factoring techniques such as grouping if necessary.
Reattempt the problem step by step to ensure you have completely factored the expression.
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