Which of the following options could be a denominator for a rational expression?
Option #1: x^2−x^0.5
Option #2: 8x^14
Option #3: 5
(1 point)
Option #
1, 2, and 3
Option #2: 8x^14 could be a denominator for a rational expression.
To determine which of the given options could be a denominator for a rational expression, we need to understand what a rational expression is.
A rational expression is a fraction where both the numerator and the denominator are polynomials. In other words, the numerator and denominator are algebraic expressions that can contain variables, constants, and exponents.
Now, let's analyze each option to see if they fit the criteria of a denominator for a rational expression:
Option #1: x^2 - x^0.5
This is a polynomial expression with two terms, x^2 and -x^0.5. However, the presence of a fractional exponent (-0.5) in the term x^0.5 makes it non-polynomial. Since the denominator in a rational expression needs to be a polynomial, Option #1 is not a valid choice.
Option #2: 8x^14
This is a polynomial expression with one term, 8x^14. It contains a variable (x) raised to a non-negative integer exponent (14). Therefore, Option #2 is a valid choice and can be a denominator for a rational expression.
Option #3: 5
This is a constant, meaning it is not a variable and does not contain any exponents. A constant can also be considered a polynomial because it is a special case of a polynomial with a degree of 0. Therefore, Option #3 is also a valid choice and can be a denominator for a rational expression.
In summary, both Option #2 (8x^14) and Option #3 (5) could be denominators for a rational expression.