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,...
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![**Question:**
Which of the following expressions is a factor of \( x^2 - 64 \)?
- A. \( x - 4 \)
- B. \( x + 4 \)
- C. \( x + 64 \)
- D. \( x^2 + 16 \)
- E. \( x^2 - 4x + 16 \)
**Explanation:**
To solve this problem, we recognize that \( x^2 - 64 \) is a difference of squares. It can be factored as follows:
\[ x^2 - 64 = (x - 8)(x + 8) \]
Therefore, neither option directly matches \( x - 8 \) or \( x + 8 \), indicating that there is no direct factor among the given choices as the expression \( x^2 - 64 \) factors into. However, options A and B can be linked to this form as they are simple factors related to differences of constant values around 8.
This is a conceptual illustration meant to review factorization techniques, especially the difference of squares. For exact matches in factor choices, a re-examination or additional context might be necessary to align with available options.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F502d0e47-5e28-4152-9f3d-16a57d4f1075%2Fee049313-d479-4dfb-8759-7e9d4552793f%2F5hvweoa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Which of the following expressions is a factor of \( x^2 - 64 \)?
- A. \( x - 4 \)
- B. \( x + 4 \)
- C. \( x + 64 \)
- D. \( x^2 + 16 \)
- E. \( x^2 - 4x + 16 \)
**Explanation:**
To solve this problem, we recognize that \( x^2 - 64 \) is a difference of squares. It can be factored as follows:
\[ x^2 - 64 = (x - 8)(x + 8) \]
Therefore, neither option directly matches \( x - 8 \) or \( x + 8 \), indicating that there is no direct factor among the given choices as the expression \( x^2 - 64 \) factors into. However, options A and B can be linked to this form as they are simple factors related to differences of constant values around 8.
This is a conceptual illustration meant to review factorization techniques, especially the difference of squares. For exact matches in factor choices, a re-examination or additional context might be necessary to align with available options.
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