5. Use long division to do this problem. Specify the quotient and remainder (10x -x- 15) (2x – 3) Find all real zeros of 6r 1 25r3 13x 1 2 0 Use the Pational Zoro TH etart
5. Use long division to do this problem. Specify the quotient and remainder (10x -x- 15) (2x – 3) Find all real zeros of 6r 1 25r3 13x 1 2 0 Use the Pational Zoro TH etart
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Mathematics Problems: Polynomial Division and Finding Zeros**
1. **Long Division of Polynomials**
**Problem 5:** Use long division to solve this problem. Specify the quotient and remainder:
\[
(10x^2 - x - 15) \div (2x - 3)
\]
2. **Finding Real Zeros of a Polynomial**
**Problem 6:** Find all real zeros of the polynomial:
\[
6x^4 + 25x^3 - 8x^2 - 43x + 20
\]
Use the Rational Zero Theorem to get started.
---
**Explanation of Graph and Diagram:**
The image includes a graph with a red curve intersecting the x-axis, indicating a possible zero at approximately (-1). The graph provides a visual understanding of the polynomial's behavior, showing points where it crosses or touches the x-axis.
**Instructions for Solving:**
- For Problem 5, apply the polynomial long division method. Divide the polynomials step-by-step, comparing degrees, and subtracting appropriately to find both the quotient and remainder.
- For Problem 6, start with the Rational Zero Theorem to list possible rational zeros. Then, test these values or use synthetic division to find the actual zeros. Consider using graphing for visual verification of results.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf8e267e-10e5-42d7-8fd7-a8f3672a74ed%2F3caccc2c-a38f-49c3-b8a1-3b55cc7a3ad1%2Fek3c5rd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Mathematics Problems: Polynomial Division and Finding Zeros**
1. **Long Division of Polynomials**
**Problem 5:** Use long division to solve this problem. Specify the quotient and remainder:
\[
(10x^2 - x - 15) \div (2x - 3)
\]
2. **Finding Real Zeros of a Polynomial**
**Problem 6:** Find all real zeros of the polynomial:
\[
6x^4 + 25x^3 - 8x^2 - 43x + 20
\]
Use the Rational Zero Theorem to get started.
---
**Explanation of Graph and Diagram:**
The image includes a graph with a red curve intersecting the x-axis, indicating a possible zero at approximately (-1). The graph provides a visual understanding of the polynomial's behavior, showing points where it crosses or touches the x-axis.
**Instructions for Solving:**
- For Problem 5, apply the polynomial long division method. Divide the polynomials step-by-step, comparing degrees, and subtracting appropriately to find both the quotient and remainder.
- For Problem 6, start with the Rational Zero Theorem to list possible rational zeros. Then, test these values or use synthetic division to find the actual zeros. Consider using graphing for visual verification of results.
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