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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![### Finding the Greatest Common Factor (GCF) of Monomials
To determine the greatest common factor of the following monomials:
\[ 21g^3h \quad \text{and} \quad 45g^3h^2 \]
### Steps to Find the GCF:
1. **Factorize the Coefficients:**
- \(21\) can be factorized into \(3 \times 7\)
- \(45\) can be factorized into \(3 \times 3 \times 5\)
- The GCF of \(21\) and \(45\) is \(3\), because \(3\) is the highest common factor.
2. **Determine the Lowest Power for Common Variables:**
- Identify the common variables \(g\) and \(h\).
- For \(g\), both monomials have the term \(g^3\), so the common term remains \(g^3\).
- For \(h\), the lowest power between \(h^1\) (from \(21g^3h\)) and \(h^2\) (from \(45g^3h^2\)) is \(h^1\) or simply \(h\).
### Combined GCF:
Combining these factors together, the GCF of the monomials \(21g^3h\) and \(45g^3h^2\) is:
\[ 3g^3h \]
### Input Instructions:
Please provide the greatest common factor in the input box provided. If you need additional symbols or functions, use the buttons available below the input field:
- `+` : Plus
- `-` : Minus
- `o` : Circle button (Unused in this scenario)
- `↵` : Arrow button for clearing input
- `?` : Help button for additional support
Once you have entered the correct answer, click the "DONE" button to submit your response.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71682d1d-4cc2-4d9e-ab7a-8c92ae915356%2Fbba70de9-fef4-47b0-b6b8-fbe89f1066ef%2Frhlp5r7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Greatest Common Factor (GCF) of Monomials
To determine the greatest common factor of the following monomials:
\[ 21g^3h \quad \text{and} \quad 45g^3h^2 \]
### Steps to Find the GCF:
1. **Factorize the Coefficients:**
- \(21\) can be factorized into \(3 \times 7\)
- \(45\) can be factorized into \(3 \times 3 \times 5\)
- The GCF of \(21\) and \(45\) is \(3\), because \(3\) is the highest common factor.
2. **Determine the Lowest Power for Common Variables:**
- Identify the common variables \(g\) and \(h\).
- For \(g\), both monomials have the term \(g^3\), so the common term remains \(g^3\).
- For \(h\), the lowest power between \(h^1\) (from \(21g^3h\)) and \(h^2\) (from \(45g^3h^2\)) is \(h^1\) or simply \(h\).
### Combined GCF:
Combining these factors together, the GCF of the monomials \(21g^3h\) and \(45g^3h^2\) is:
\[ 3g^3h \]
### Input Instructions:
Please provide the greatest common factor in the input box provided. If you need additional symbols or functions, use the buttons available below the input field:
- `+` : Plus
- `-` : Minus
- `o` : Circle button (Unused in this scenario)
- `↵` : Arrow button for clearing input
- `?` : Help button for additional support
Once you have entered the correct answer, click the "DONE" button to submit your response.
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