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
![### Polynomial Equation Solutions
**Objective:**
Find all the solutions to each equation.
**Problem:**
A. \((2x + 1)(x + 8) = 0\)
#### Explanation:
To solve the equation \((2x + 1)(x + 8) = 0\), you need to find the values of \(x\) that make the equation true. This involves setting each factor equal to zero and solving for \(x\).
1. **First Factor: \(2x + 1 = 0\)**
- Solve for \(x\):
\[
2x + 1 = 0 \implies 2x = -1 \implies x = -\frac{1}{2}
\]
2. **Second Factor: \(x + 8 = 0\)**
- Solve for \(x\):
\[
x + 8 = 0 \implies x = -8
\]
Thus, the solutions to the equation \((2x + 1)(x + 8) = 0\) are:
\[
x = -\frac{1}{2} \quad \text{and} \quad x = -8
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fedcacc2f-3b65-4c4b-8e45-a833a57afce3%2F730d2ff0-e37e-4f39-936a-14bd868a55ac%2F9qusaxg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Polynomial Equation Solutions
**Objective:**
Find all the solutions to each equation.
**Problem:**
A. \((2x + 1)(x + 8) = 0\)
#### Explanation:
To solve the equation \((2x + 1)(x + 8) = 0\), you need to find the values of \(x\) that make the equation true. This involves setting each factor equal to zero and solving for \(x\).
1. **First Factor: \(2x + 1 = 0\)**
- Solve for \(x\):
\[
2x + 1 = 0 \implies 2x = -1 \implies x = -\frac{1}{2}
\]
2. **Second Factor: \(x + 8 = 0\)**
- Solve for \(x\):
\[
x + 8 = 0 \implies x = -8
\]
Thus, the solutions to the equation \((2x + 1)(x + 8) = 0\) are:
\[
x = -\frac{1}{2} \quad \text{and} \quad x = -8
\]
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