Question

Which of these is a polynomial? [Select all that apply.](2 points) Responses 5x2+x4 5 x squared plus x to the 4th power x2+4x−5 x squared plus 4 x minus 5 9x−2+3x 9 x to the negative 2 power plus 3 x 2x13+5

Answer 1

To determine which of the given expressions are polynomials, we need to remember that a polynomial is defined as an expression consisting of variables raised to non-negative integer powers and combined using addition, subtraction, and multiplication. Expressions that include variables raised to negative powers or roots are not polynomials.

Let's analyze the provided expressions:

1. **5x² + x⁴** - This is a polynomial because both terms have non-negative integer powers.

2. **x² + 4x - 5** - This is also a polynomial since all the terms involve non-negative integer powers.

3. **9x⁻² + 3x** - This is **not** a polynomial because the term 9x⁻² includes a negative exponent.

4. **2x¹³ + 5** - This is a polynomial as both terms involve non-negative integer powers (x¹³ and the constant 5).

Therefore, the polynomials are:

- **5x² + x⁴**
- **x² + 4x - 5**
- **2x¹³ + 5**