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**
**Problem:**
Factor the polynomial given below:
\[
\frac{1}{7}x^3 - \frac{4}{35}x^2
\]
In the expression above, you need to identify any common factors and factor them out.
**Solution:**
1. **Identify the Greatest Common Factor (GCF):**
- The coefficients are \(\frac{1}{7}\) and \(\frac{4}{35}\).
- The common factor for \(\frac{1}{7}\) and \(\frac{4}{35}\) is \(\frac{1}{35}\).
- The common factor for the variable terms \(x^3\) and \(x^2\) is \(x^2\).
2. **Factor Out the GCF:**
- The GCF of the overall expression is \(\frac{1}{35}x^2\).
- Factoring this out gives:
\[
\frac{1}{35}x^2 \left( 5x - 4 \right)
\]
3. **Type Your Answer:**
In factored form, the polynomial is:
\[
\frac{1}{35}x^2 (5x - 4)
\]
Remember to simplify every term and check your work by multiplying the factors back together to ensure you get the original expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F841a23ff-64ca-4d99-a92f-2adfa7b3fe4f%2F95706a2f-e9d8-481c-a85c-d1366d9ea223%2Fkdetp1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Factoring Polynomials**
**Problem:**
Factor the polynomial given below:
\[
\frac{1}{7}x^3 - \frac{4}{35}x^2
\]
In the expression above, you need to identify any common factors and factor them out.
**Solution:**
1. **Identify the Greatest Common Factor (GCF):**
- The coefficients are \(\frac{1}{7}\) and \(\frac{4}{35}\).
- The common factor for \(\frac{1}{7}\) and \(\frac{4}{35}\) is \(\frac{1}{35}\).
- The common factor for the variable terms \(x^3\) and \(x^2\) is \(x^2\).
2. **Factor Out the GCF:**
- The GCF of the overall expression is \(\frac{1}{35}x^2\).
- Factoring this out gives:
\[
\frac{1}{35}x^2 \left( 5x - 4 \right)
\]
3. **Type Your Answer:**
In factored form, the polynomial is:
\[
\frac{1}{35}x^2 (5x - 4)
\]
Remember to simplify every term and check your work by multiplying the factors back together to ensure you get the original expression.
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