Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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![**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.](https://content.bartleby.com/qna-images/question/841a23ff-64ca-4d99-a92f-2adfa7b3fe4f/95706a2f-e9d8-481c-a85c-d1366d9ea223/kdetp1_processed.jpeg)
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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