Question

Which of the following options could be a denominator for a rational expression?

Option #1: x2−x0.5


Option #2: 8x14


Option #3: 5

(1 point)
Option #

Answer 1

To determine which option could be a denominator for a rational expression, we need to ensure that the denominator is a polynomial expression.

1. **Option #1: \( x^2 - x^{0.5} \)**
This expression is not a polynomial because it contains a term with a fractional exponent (\( x^{0.5} \)). Therefore, it cannot be used as a denominator for a rational expression.

2. **Option #2: \( 8x^{14} \)**
This expression is a polynomial since it is of the form \( ax^n \), where \( a \) is a constant and \( n \) is a non-negative integer. It can be used as a denominator for a rational expression.

3. **Option #3: 5**
This is a constant, which can also be viewed as a polynomial of degree 0. Thus, it can also be used as a denominator for a rational expression.

Based on this analysis, the options that could serve as denominators for a rational expression are:

- Option #2: \( 8x^{14} \)
- Option #3: 5

If you need to select one option that qualifies, the best choice would be **Option #2: \( 8x^{14} \)**, but both Options #2 and #3 are valid denominators.