Question
Which expressions are polynomials?
Select each correct answer.
Responses
6x² + 5x
6 x ² + 5 x
x2+5x15
x squared plus 5 x begin power 1 fifth end power
−7x2+53x
negative 7 x squared plus begin fraction 5 over 3x end fraction
−x2+5x
negative x squared plus 5 x
Select each correct answer.
Responses
6x² + 5x
6 x ² + 5 x
x2+5x15
x squared plus 5 x begin power 1 fifth end power
−7x2+53x
negative 7 x squared plus begin fraction 5 over 3x end fraction
−x2+5x
negative x squared plus 5 x
Answers
GPT-4o mini
To determine which expressions are polynomials, we need to understand that a polynomial is a mathematical expression that consists of variables raised to non-negative integer powers, with coefficients that are real numbers.
Let's evaluate each expression:
1. **6x² + 5x**: This is a polynomial because it consists of terms (6x² and 5x) with non-negative integer powers.
2. **6 x ² + 5 x**: This is also a polynomial and represents the same expression as the first one.
3. **x2+5x15**: This expression does not clearly follow standard polynomial notation due to the "5x15" part, which suggests multiplication (5 times x raised to the 15th power). If interpreted as "5x to the power of 15", it's a polynomial. If interpreted as a multiplication of x and 15, it could cause confusion, but typically, it's not a standard form of a polynomial. Hence, this could be ambiguous.
4. **−7x2+53x**: If "53x" is interpreted simply as a term (noting it should be "5/3x" as a fraction), it looks like a polynomial. However, if taken literally as "53x" and extra, it's not properly formatted. It seems correct if "5/3" was meant.
5. **−x2+5x**: This is a polynomial because it consists of terms (−x² and 5x) with non-negative integer powers.
Considering the definitions:
The correct polynomial expressions from the provided options are:
- **6x² + 5x**
- **6 x ² + 5 x**
- **−x2 + 5x**
(Regarding the third and fourth interpretations, they require clarification or correction.)
Let's evaluate each expression:
1. **6x² + 5x**: This is a polynomial because it consists of terms (6x² and 5x) with non-negative integer powers.
2. **6 x ² + 5 x**: This is also a polynomial and represents the same expression as the first one.
3. **x2+5x15**: This expression does not clearly follow standard polynomial notation due to the "5x15" part, which suggests multiplication (5 times x raised to the 15th power). If interpreted as "5x to the power of 15", it's a polynomial. If interpreted as a multiplication of x and 15, it could cause confusion, but typically, it's not a standard form of a polynomial. Hence, this could be ambiguous.
4. **−7x2+53x**: If "53x" is interpreted simply as a term (noting it should be "5/3x" as a fraction), it looks like a polynomial. However, if taken literally as "53x" and extra, it's not properly formatted. It seems correct if "5/3" was meant.
5. **−x2+5x**: This is a polynomial because it consists of terms (−x² and 5x) with non-negative integer powers.
Considering the definitions:
The correct polynomial expressions from the provided options are:
- **6x² + 5x**
- **6 x ² + 5 x**
- **−x2 + 5x**
(Regarding the third and fourth interpretations, they require clarification or correction.)