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
![**Topic: Factoring Polynomials**
**Objective:** Factor out the greatest common factor from the polynomial.
**Problem Statement:**
Given the polynomial:
\[
-15p^3 + 25p^2 + 35p
\]
**Task:** Factor out the greatest common factor (GCF).
**Solution Approach:**
1. **Identify the GCF of the coefficients:**
- The coefficients are -15, 25, and 35.
- The GCF of these numbers is 5.
2. **Identify the lowest power of \( p \):**
- The terms are \( p^3 \), \( p^2 \), and \( p^1 \).
- The lowest power is \( p^1 \).
3. **Factor out the GCF:**
- Factor out \( 5p \) from each term:
\[
-15p^3 = -5p \cdot 3p^2
\]
\[
25p^2 = 5p \cdot 5p
\]
\[
35p = 5p \cdot 7
\]
4. **Rewrite the polynomial:**
Final expression after factoring:
\[
-15p^3 + 25p^2 + 35p = 5p(-3p^2 + 5p + 7)
\]
**Answer Box:**
\[
5p(-3p^2 + 5p + 7)
\]
(Type your answer in the box provided.)
---
**Note:** Factoring polynomials by finding the greatest common factor is a foundational algebra skill that simplifies expressions and solves equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F841a23ff-64ca-4d99-a92f-2adfa7b3fe4f%2Fb181db3f-d8c3-4b08-8939-1f6fb8a38d48%2F1xjlpfh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Factoring Polynomials**
**Objective:** Factor out the greatest common factor from the polynomial.
**Problem Statement:**
Given the polynomial:
\[
-15p^3 + 25p^2 + 35p
\]
**Task:** Factor out the greatest common factor (GCF).
**Solution Approach:**
1. **Identify the GCF of the coefficients:**
- The coefficients are -15, 25, and 35.
- The GCF of these numbers is 5.
2. **Identify the lowest power of \( p \):**
- The terms are \( p^3 \), \( p^2 \), and \( p^1 \).
- The lowest power is \( p^1 \).
3. **Factor out the GCF:**
- Factor out \( 5p \) from each term:
\[
-15p^3 = -5p \cdot 3p^2
\]
\[
25p^2 = 5p \cdot 5p
\]
\[
35p = 5p \cdot 7
\]
4. **Rewrite the polynomial:**
Final expression after factoring:
\[
-15p^3 + 25p^2 + 35p = 5p(-3p^2 + 5p + 7)
\]
**Answer Box:**
\[
5p(-3p^2 + 5p + 7)
\]
(Type your answer in the box provided.)
---
**Note:** Factoring polynomials by finding the greatest common factor is a foundational algebra skill that simplifies expressions and solves equations.
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