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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Transcribed Image Text:When a polynomial is divided by \(3x + 5\), the quotient is \(6x - 5\) and the remainder is \(-7\). What is the dividend?
![**Problem Statement:**
When a polynomial is divided by (6x + 1), the quotient is (2x - 3) with a remainder of -9. What is the dividend?
**Solution:**
The formula for polynomial division is given by:
\[ \frac{\text{Dividend}}{6x + 1} = (2x - 3) - 9 \]
To find the Dividend, we rearrange using:
\[ \text{Dividend} = (6x + 1)(2x - 3) - 9 \]
**Step-by-Step Calculation:**
1. **Expand the product:**
\[
(6x + 1)(2x - 3) = 12x^2 - 18x + 2x - 3
\]
2. **Simplify:**
\[
= 12x^2 - 16x - 3
\]
3. **Subtract the remainder:**
\[
12x^2 - 16x - 3 - 9 = 12x^2 - 16x - 12
\]
**Dividend:**
The dividend of the polynomial is \( 12x^2 - 16x - 12 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc15101c2-474b-4f60-bc6d-0f6959326517%2Fd2ec38b4-63bf-460f-83ad-c8a9c14905bc%2F0rk2uef_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
When a polynomial is divided by (6x + 1), the quotient is (2x - 3) with a remainder of -9. What is the dividend?
**Solution:**
The formula for polynomial division is given by:
\[ \frac{\text{Dividend}}{6x + 1} = (2x - 3) - 9 \]
To find the Dividend, we rearrange using:
\[ \text{Dividend} = (6x + 1)(2x - 3) - 9 \]
**Step-by-Step Calculation:**
1. **Expand the product:**
\[
(6x + 1)(2x - 3) = 12x^2 - 18x + 2x - 3
\]
2. **Simplify:**
\[
= 12x^2 - 16x - 3
\]
3. **Subtract the remainder:**
\[
12x^2 - 16x - 3 - 9 = 12x^2 - 16x - 12
\]
**Dividend:**
The dividend of the polynomial is \( 12x^2 - 16x - 12 \).
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