Question
Which expressions are polynomials?
Select each correct answer.
Responses
x2+5x15
x squared plus 5 x begin power 1 fifth end power
6x² + 5x
6 x ² + 5 x
−7x2+53x
negative 7 x squared plus begin fraction 5 over 3x end fraction
−x2+5x
Select each correct answer.
Responses
x2+5x15
x squared plus 5 x begin power 1 fifth end power
6x² + 5x
6 x ² + 5 x
−7x2+53x
negative 7 x squared plus begin fraction 5 over 3x end fraction
−x2+5x
Answers
GPT-4o mini
To determine which expressions are polynomials, we evaluate each option based on the characteristics of polynomials. A polynomial is a mathematical expression that consists of variables raised to non-negative integer powers and coefficients.
1. **x² + 5x¹/5**: This expression includes \(x^{1/5}\), which is a fractional exponent, thus it is **not** a polynomial.
2. **6x² + 5x**: This expression consists of terms with non-negative integer exponents (2 and 1). Therefore, it **is** a polynomial.
3. **−7x² + \frac{5}{3}x**: This expression involves non-negative integer powers of \(x\) (2 and 1) and a constant coefficient. Thus, it **is** a polynomial.
4. **−x² + 5x**: This expression has non-negative integer powers of \(x\) (2 and 1). Therefore, it **is** a polynomial.
In summary, the expressions that are polynomials are:
- **6x² + 5x**
- **−7x² + \frac{5}{3}x**
- **−x² + 5x**
1. **x² + 5x¹/5**: This expression includes \(x^{1/5}\), which is a fractional exponent, thus it is **not** a polynomial.
2. **6x² + 5x**: This expression consists of terms with non-negative integer exponents (2 and 1). Therefore, it **is** a polynomial.
3. **−7x² + \frac{5}{3}x**: This expression involves non-negative integer powers of \(x\) (2 and 1) and a constant coefficient. Thus, it **is** a polynomial.
4. **−x² + 5x**: This expression has non-negative integer powers of \(x\) (2 and 1). Therefore, it **is** a polynomial.
In summary, the expressions that are polynomials are:
- **6x² + 5x**
- **−7x² + \frac{5}{3}x**
- **−x² + 5x**