Question
Which are polynomials and which are not?
8x^10+2x^5
x^2-√x-3
4-3x+5x^6
14x^7
8x^10+2x^5
x^2-√x-3
4-3x+5x^6
14x^7
Answers
Answered by
GPT-4o mini
To determine which expressions are polynomials, we need to consider the definition of a polynomial. A polynomial is an expression that consists of variables raised to non-negative integer exponents and coefficients that are real numbers.
Let's evaluate each expression:
1. **8x^10 + 2x^5**: This expression consists of terms with non-negative integer exponents (10 and 5). Therefore, it is a polynomial.
2. **x^2 - √x - 3**: The term √x can be rewritten as x^(1/2), which is not a non-negative integer exponent (it is a positive fraction). Therefore, this expression is **not a polynomial**.
3. **4 - 3x + 5x^6**: This expression contains terms with non-negative integer exponents (0 for 4, 1 for -3x, and 6 for 5x^6). Therefore, it is a polynomial.
4. **14x^7**: This is a single term with a non-negative integer exponent (7). Therefore, it is a polynomial.
In summary:
- Polynomials: 8x^10 + 2x^5, 4 - 3x + 5x^6, 14x^7
- Not a polynomial: x^2 - √x - 3
Let's evaluate each expression:
1. **8x^10 + 2x^5**: This expression consists of terms with non-negative integer exponents (10 and 5). Therefore, it is a polynomial.
2. **x^2 - √x - 3**: The term √x can be rewritten as x^(1/2), which is not a non-negative integer exponent (it is a positive fraction). Therefore, this expression is **not a polynomial**.
3. **4 - 3x + 5x^6**: This expression contains terms with non-negative integer exponents (0 for 4, 1 for -3x, and 6 for 5x^6). Therefore, it is a polynomial.
4. **14x^7**: This is a single term with a non-negative integer exponent (7). Therefore, it is a polynomial.
In summary:
- Polynomials: 8x^10 + 2x^5, 4 - 3x + 5x^6, 14x^7
- Not a polynomial: x^2 - √x - 3