Question

Which expressions are polynomials?

Select each correct answer.



Responses

8x−z3
8 x minus z cubed

x−1
x minus 1

6 + p
6 + p

5x2−x√

Answer 1

To determine which expressions are polynomials, we need to check if they conform to the definition of a polynomial. A polynomial in one variable consists of variables raised to non-negative integer powers and has coefficients that are real numbers (including zero).

Let's analyze each expression:

1. **8x - z³**: This expression is a polynomial in terms of two variables (x and z). The term 8x is a polynomial term and z³ is also a polynomial term since the exponent is a non-negative integer. **This is a polynomial.**

2. **x - 1**: This expression is a simple polynomial of degree 1. It consists of a single variable x raised to the first power and a constant term (-1). **This is a polynomial.**

3. **6 + p**: This expression is also a polynomial. It can be considered a polynomial in the variable p of degree 1. It consists of a constant term (6) and a linear term (p). **This is a polynomial.**

4. **5x² - x√**: The term "x√" means x raised to the power of 1/2 (which is a square root). Since polynomials can only have non-negative integer exponents (0, 1, 2, etc.), having a term like x^(1/2) means this is not a polynomial. **This is not a polynomial.**

In summary, the correct polynomial expressions are:

- **8x − z³**
- **x − 1**
- **6 + p**