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
how do you factor

Transcribed Image Text:**Title: Using a Step-by-Step Calculator for Factoring Polynomials**
**Overview:**
This educational guide demonstrates how to use an online tool for factoring cubic polynomials. It uses the example polynomial \(x^3 + x^2 - 7x - 15\) to show the step-by-step process.
**Process:**
1. **Polynomial Input:**
- The polynomial to be factored is entered into the calculator: \(x^3 + x^2 - 7x - 15\).
2. **Factoring:**
- The tool factors the polynomial as \( (x - 3)(x^2 + 4x + 5) \).
3. **Steps Explained:**
- **Initial Equation:** \(x^3 + x^2 - 7x - 15\).
- **Rational Root Theorem Applied:**
- The theorem is used to identify potential rational roots of the polynomial.
- The rational root theorem helps determine the roots by testing possible values derived from the coefficients.
4. **Solution Details:**
- The polynomial is factored into two components: one linear \((x - 3)\) and one quadratic \((x^2 + 4x + 5)\).
**Related Features:**
- **Graphing and Solver Tools:** The calculator may provide graphing features and further solutions, such as solving for roots or analyzing the polynomial's behavior.
- **Learning Support:** A related blog with tips on improving mathematical skills, emphasizing practice and dedication.
**Practical Application:**
- Utilizing factoring techniques is essential for solving polynomial equations, which is pivotal in algebra and calculus courses. The step-by-step approach ensures better understanding and retention of mathematical concepts.
This guide should enable users to understand not just how to factor a polynomial using an online calculator, but also the underlying mathematical principles such as the application of the rational root theorem.
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