5) 8x6 + 6x3 + 20x3. + 15

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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Factor completely 

### Polynomial Equation Example

In this example, we are given a polynomial equation which is as follows:

\[ 8x^6 + 6x^3 + 20x^3 + 15 \]

Here is a breakdown of each term within the equation:

1. **\(8x^6\)**: This term represents 8 times \(x\) raised to the power of 6.
2. **\(6x^3\)**: This term denotes 6 times \(x\) raised to the power of 3.
3. **\(20x^3\)**: This term signifies 20 times \(x\) raised to the power of 3.
4. **15**: This is a constant term without any variable attached to it.

### Key Points to Note:

- **Degree of the Polynomial**: The highest power of the variable \(x\) in the polynomial is 6 (from the term \(8x^6\)). Therefore, this is a polynomial of degree 6.
- **Like Terms**: Notice that \(6x^3\) and \(20x^3\) are like terms, and they can be combined to simplify the polynomial further.

To simplify the polynomial:

\[ 8x^6 + (6x^3 + 20x^3) + 15 \]
\[ 8x^6 + 26x^3 + 15 \]

This produces a more simplified version of the polynomial equation. This summary is useful for understanding the composition and simplification of polynomial expressions, which is a fundamental concept in algebra.
Transcribed Image Text:### Polynomial Equation Example In this example, we are given a polynomial equation which is as follows: \[ 8x^6 + 6x^3 + 20x^3 + 15 \] Here is a breakdown of each term within the equation: 1. **\(8x^6\)**: This term represents 8 times \(x\) raised to the power of 6. 2. **\(6x^3\)**: This term denotes 6 times \(x\) raised to the power of 3. 3. **\(20x^3\)**: This term signifies 20 times \(x\) raised to the power of 3. 4. **15**: This is a constant term without any variable attached to it. ### Key Points to Note: - **Degree of the Polynomial**: The highest power of the variable \(x\) in the polynomial is 6 (from the term \(8x^6\)). Therefore, this is a polynomial of degree 6. - **Like Terms**: Notice that \(6x^3\) and \(20x^3\) are like terms, and they can be combined to simplify the polynomial further. To simplify the polynomial: \[ 8x^6 + (6x^3 + 20x^3) + 15 \] \[ 8x^6 + 26x^3 + 15 \] This produces a more simplified version of the polynomial equation. This summary is useful for understanding the composition and simplification of polynomial expressions, which is a fundamental concept in algebra.
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