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
![**Factor by Grouping**
Given expression:
\[ x^3 - 5x^2 + 4x - 20 \]
Objective: Factor the polynomial by grouping.
---
**Explanation:**
The expression shown is a polynomial of degree 3. To factor by grouping, you look for common factors in groups of terms. In this expression:
1. Group the terms:
- \((x^3 - 5x^2)\) and \((4x - 20)\).
2. Factor out the greatest common factor from each group:
- From \((x^3 - 5x^2)\), factor out \(x^2\).
- From \((4x - 20)\), factor out 4.
3. The expression becomes:
\[ x^2(x - 5) + 4(x - 5) \]
4. Notice the common factor \((x - 5)\):
- Combine them to get the factored form:
\[ (x^2 + 4)(x - 5) \]
The factored form of the polynomial is \((x^2 + 4)(x - 5)\).
**Note:** The provided box in the image is meant for the answer, where you enter the factored expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F841a23ff-64ca-4d99-a92f-2adfa7b3fe4f%2Febced1dd-e1b5-4e08-9b98-b391bb5e0a60%2Fajhtozd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Factor by Grouping**
Given expression:
\[ x^3 - 5x^2 + 4x - 20 \]
Objective: Factor the polynomial by grouping.
---
**Explanation:**
The expression shown is a polynomial of degree 3. To factor by grouping, you look for common factors in groups of terms. In this expression:
1. Group the terms:
- \((x^3 - 5x^2)\) and \((4x - 20)\).
2. Factor out the greatest common factor from each group:
- From \((x^3 - 5x^2)\), factor out \(x^2\).
- From \((4x - 20)\), factor out 4.
3. The expression becomes:
\[ x^2(x - 5) + 4(x - 5) \]
4. Notice the common factor \((x - 5)\):
- Combine them to get the factored form:
\[ (x^2 + 4)(x - 5) \]
The factored form of the polynomial is \((x^2 + 4)(x - 5)\).
**Note:** The provided box in the image is meant for the answer, where you enter the factored expression.
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