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
![**1. Synthetic Division**
Use synthetic division to determine whether \(-2\) is a zero of \(f(x) = x^3 + 4x^2 + x - 6\). Answer yes or no. Show your work.
---
**2. Polynomial Long Division**
Use long division to find the quotient \(Q(x)\) and the remainder \(R(x)\) when \(P(x)\) is divided by \(d(x)\). Express \(P(x)\) in the form \(d(x) \cdot Q(x) + R(x)\). Show your work.
\[P(x) = x^4 + 3x^3 + 2x - 5\]
\[d(x) = x - 1\]
---
**3. Graph Identification**
The graph of \(f(x) = x^3 - x^2 - 2\) is which of the following?
- **Graph A:** Shows a graph with an inflection point and increasing behavior in both directions, but a decrease in the middle interval.
- **Graph B:** Illustrates a behavior similar to a cubic function potentially with two turning points, and overall increases from left to right.
- **Graph C:** Presents another possibility for a cubic graph, showing one turning point and a change in direction.
- **Graph D:** Demonstrates a graph that increases initially, then decreases slightly, before increasing again, indicative of cubic behavior with one inflection point.
(Note: The graphs are visual diagrams indicating different possible shapes of polynomial functions, characterized by their turning points and end behaviors typical of cubic equations.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1b7a372-1344-4f7f-af15-7d7e9d0720e7%2F844844a0-deef-4da0-ab2e-3c53b3e41d22%2F1h2x9xl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**1. Synthetic Division**
Use synthetic division to determine whether \(-2\) is a zero of \(f(x) = x^3 + 4x^2 + x - 6\). Answer yes or no. Show your work.
---
**2. Polynomial Long Division**
Use long division to find the quotient \(Q(x)\) and the remainder \(R(x)\) when \(P(x)\) is divided by \(d(x)\). Express \(P(x)\) in the form \(d(x) \cdot Q(x) + R(x)\). Show your work.
\[P(x) = x^4 + 3x^3 + 2x - 5\]
\[d(x) = x - 1\]
---
**3. Graph Identification**
The graph of \(f(x) = x^3 - x^2 - 2\) is which of the following?
- **Graph A:** Shows a graph with an inflection point and increasing behavior in both directions, but a decrease in the middle interval.
- **Graph B:** Illustrates a behavior similar to a cubic function potentially with two turning points, and overall increases from left to right.
- **Graph C:** Presents another possibility for a cubic graph, showing one turning point and a change in direction.
- **Graph D:** Demonstrates a graph that increases initially, then decreases slightly, before increasing again, indicative of cubic behavior with one inflection point.
(Note: The graphs are visual diagrams indicating different possible shapes of polynomial functions, characterized by their turning points and end behaviors typical of cubic equations.)
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