Question

Which expressions are polynomials?

Select each correct answer.



Responses

2 + s
2 + s

y
y

x2−x√+2
x squared minus square root x end root plus 2

4x³ + y

Answer 1

To determine which expressions are polynomials, we need to check if they meet the criteria for polynomials:

1. A polynomial can contain variables raised to non-negative integer exponents.
2. It can include coefficients, which are typically real or complex numbers.
3. It cannot have variables in the denominator, under a square root, or in any negative exponent.

Now, let's analyze each option:

1. **2 + s**: This is a polynomial. It has a constant term (2) and a linear term (s).

2. **y**: This is also a polynomial. It can be considered as \(0y^n\) where n=1.

3. **x²−x√+2**: This is not a polynomial because \( \sqrt{x} \) can be rewritten as \( x^{1/2} \), which has a non-integer exponent. Therefore, this expression does not qualify as a polynomial.

4. **4x³ + y**: This is a polynomial as it contains a cubic term \(4x^3\) and a linear term in \(y\).

Based on this analysis, the correct responses that are polynomials are:

1. 2 + s
2. y
4. 4x³ + y