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