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
![**Question 5 of 10**
Use long division to find the quotient below.
\[
(15x^3 + 2x^2 - 75) \div (3x - 5)
\]
**Options:**
A. \(5x^2 - 12x + 15\)
B. \(5x^2 + 9x + 15\)
C. \(5x^2 + 12x + 15\)
D. \(5x^2 - 9x + 15\)
---
**Explanation for Each Option:**
- **Option A:** This option suggests that the quotient of the long division will result in \(5x^2 - 12x + 15\).
- **Option B:** This option suggests that the quotient of the long division will result in \(5x^2 + 9x + 15\).
- **Option C:** This option suggests that the quotient of the long division will result in \(5x^2 + 12x + 15\).
- **Option D:** This option suggests that the quotient of the long division will result in \(5x^2 - 9x + 15\).
### Instructions for Students:
To find the correct quotient, follow these steps:
1. **Set up the Division:** Write \(15x^3 + 2x^2 - 75\) under the long division symbol and \(3x - 5\) outside of the symbol.
2. **Divide the Leading Terms:** Divide the leading term of the dividend (15x^3) by the leading term of the divisor (3x).
3. **Multiply and Subtract:** Multiply your answer from step 2 by the entire divisor (3x - 5) and subtract this product from the dividend.
4. **Repeat:** Continue this process with the new polynomial until no terms are left.
Work through the problem step-by-step to determine which option is correct.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8fdc5c45-6410-437e-ba36-45d933a9ea97%2F08338ff6-a036-4111-a03f-993b5e400a91%2Fpzwpueh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 5 of 10**
Use long division to find the quotient below.
\[
(15x^3 + 2x^2 - 75) \div (3x - 5)
\]
**Options:**
A. \(5x^2 - 12x + 15\)
B. \(5x^2 + 9x + 15\)
C. \(5x^2 + 12x + 15\)
D. \(5x^2 - 9x + 15\)
---
**Explanation for Each Option:**
- **Option A:** This option suggests that the quotient of the long division will result in \(5x^2 - 12x + 15\).
- **Option B:** This option suggests that the quotient of the long division will result in \(5x^2 + 9x + 15\).
- **Option C:** This option suggests that the quotient of the long division will result in \(5x^2 + 12x + 15\).
- **Option D:** This option suggests that the quotient of the long division will result in \(5x^2 - 9x + 15\).
### Instructions for Students:
To find the correct quotient, follow these steps:
1. **Set up the Division:** Write \(15x^3 + 2x^2 - 75\) under the long division symbol and \(3x - 5\) outside of the symbol.
2. **Divide the Leading Terms:** Divide the leading term of the dividend (15x^3) by the leading term of the divisor (3x).
3. **Multiply and Subtract:** Multiply your answer from step 2 by the entire divisor (3x - 5) and subtract this product from the dividend.
4. **Repeat:** Continue this process with the new polynomial until no terms are left.
Work through the problem step-by-step to determine which option is correct.
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