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
![**Problem:** Factor the expression completely: \( x^3 - 10x^2 + 21x \)
**Solution Box:** [ ]
To factor the expression, follow these steps:
1. **Identify the Greatest Common Factor (GCF):**
- The GCF in the terms \( x^3 \), \( -10x^2 \), and \( 21x \) is \( x \).
2. **Factor out the GCF:**
- When factoring out \( x \), you get: \( x(x^2 - 10x + 21) \).
3. **Factor the quadratic expression:**
- Find two numbers whose product is 21 and sum is -10.
- The numbers -3 and -7 satisfy these conditions.
4. **Write the complete factorization:**
- The fully factored expression is: \( x(x - 3)(x - 7) \).
Make sure to verify your answer by expanding the factors to check that they multiply back to the original expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7d591113-c73d-4bf8-a1b7-9966513ce440%2F31fcf4c3-ce1e-4fd9-9e85-0ca1e5f3f376%2F7hbsvhl_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem:** Factor the expression completely: \( x^3 - 10x^2 + 21x \)
**Solution Box:** [ ]
To factor the expression, follow these steps:
1. **Identify the Greatest Common Factor (GCF):**
- The GCF in the terms \( x^3 \), \( -10x^2 \), and \( 21x \) is \( x \).
2. **Factor out the GCF:**
- When factoring out \( x \), you get: \( x(x^2 - 10x + 21) \).
3. **Factor the quadratic expression:**
- Find two numbers whose product is 21 and sum is -10.
- The numbers -3 and -7 satisfy these conditions.
4. **Write the complete factorization:**
- The fully factored expression is: \( x(x - 3)(x - 7) \).
Make sure to verify your answer by expanding the factors to check that they multiply back to the original expression.
Expert Solution
Step 1
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education