Question
Determine if the expression \( -7 b^{4}+b^{2} \) is a polynomial or not. If it is a polynomial, state the type and degree of the polynomial. Answer Attempt 1 out of 2 The given expression
Ask by Norton Griffiths. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The expression \( -7 b^{4} + b^{2} \) is a single-variable polynomial of degree 4.
Solution
Yes, the expression \( -7 b^{4} + b^{2} \) is a **polynomial**.
### Type of Polynomial:
- **Single-variable polynomial**: The expression contains only one variable, \( b \).
### Degree of the Polynomial:
- **Degree 4**: The degree of a polynomial is determined by the highest exponent of the variable. In this case, the highest exponent is 4 (from the term \( -7 b^{4} \)).
**Summary:**
\( -7 b^{4} + b^{2} \) is a single-variable polynomial of degree 4.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
The given expression \( -7 b^{4}+b^{2} \) is indeed a polynomial! In this expression, the term \( -7 b^{4} \) has a degree of 4, while the term \( b^{2} \) has a degree of 2. Since the highest power of the variable \( b \) is 4, we classify this polynomial as a quartic polynomial, specifically of degree 4. Polynomials can be found everywhere! They pop up in physics for calculating trajectories, in finance for modeling profit curves, and even in computer graphics for creating smooth curves. This means that understanding polynomials can significantly aid in deciphering real-world phenomena, making them a crucial foundation in various fields!
