Question
10. [0/1 Points] DETAILS MY NOTES TGEIALG6 5.4.040. Find the degree of the polynomial. SUBMIT ANSWER
Ask by Wells Bradley. in the United States
Jan 24,2025
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Tutor-Verified Answer
Answer
To find the degree of a polynomial, arrange the terms in order of highest to lowest exponent and identify the term with the largest exponent. For example, in \(4x^3 - 2x^2 + 7x - 5\), the degree is 3.
Solution
Sure, I'd be happy to help you determine the degree of a polynomial. However, I'll need the specific polynomial expression to provide an accurate answer.
**In the meantime, here's a general overview:**
### What is the Degree of a Polynomial?
- **Definition:** The degree of a polynomial is the highest power of the variable \( x \) in the polynomial expression when it's written in its standard form (from highest to lowest degree).
### How to Find the Degree:
1. **Write the Polynomial in Standard Form:** Arrange the terms in descending order of the exponents of \( x \).
*Example:*
\[
4x^3 - 2x^2 + 7x - 5
\]
2. **Identify the Highest Exponent:** Look for the term with the largest exponent.
*In the example above*, the highest exponent is **3** (from \( 4x^3 \)).
3. **Determine the Degree:** The highest exponent is the degree of the polynomial.
*So, the degree is **3***.
### Example Problem:
Find the degree of the polynomial \( 6x^5 - 3x^3 + x - 8 \).
**Solution:**
1. The polynomial is already in standard form.
2. The exponents are 5, 3, 1, and 0.
3. The highest exponent is 5.
**Degree:** 5
---
**Please provide the specific polynomial** you're working with, and I'd be glad to help you find its degree!
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To find the degree of a polynomial, you need to identify the term with the highest exponent. For example, in the polynomial \(3x^4 + 2x^3 - x + 7\), the term \(3x^4\) has the highest exponent, which is 4. Therefore, the degree of this polynomial is 4! Another fun thing to remember is that if a polynomial has all its terms with the same degree, it is termed a "homogeneous polynomial." For example, \(5x^3 + 2y^3 - 4z^3\) would be a homogeneous polynomial of degree 3. So, not only can polynomials vary in degree, but they can also share the same degree across all their terms!
