Question

Which expressions are polynomials?

Select each correct answer.



Responses

6 + w
6 + w

2x4−y
2 x being power 4 end power minus y

z + 1
z + 1

y2−y√3+4

Answer 1

A polynomial is an expression that consists of variables raised to whole number (non-negative integer) powers and multiplied by coefficients.

Let's analyze the provided expressions:

1. **6 + w**: This expression is a polynomial; it contains a constant term (6) and a variable (w) raised to the power of 1.

2. **2x⁴ - y**: This expression is also a polynomial; it includes \(2x^4\) (where x is raised to the power of 4) and \(-y\) (where y is raised to the power of 1). Both terms are valid for polynomials.

3. **z + 1**: This is a polynomial as well; it consists of a variable term (z) and a constant term (1).

4. **y² - y√3 + 4**: This expression is not a polynomial because the term \(-y√3\) involves a variable y being multiplied with a non-integer power (the constant √3 is not a polynomial coefficient since it implies multiplication with a square root).

Thus, the valid polynomials from the list are:

- 6 + w
- 2x⁴ - y
- z + 1

The expression **y² - y√3 + 4** is **not** a polynomial.