Is 5^x a Valid Term in a Polynomial?

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5^x is not a valid term in a polynomial, as polynomials consist only of terms with non-negative integer exponents. The discussion clarifies that a rational function, such as y=(5x^4 + 5^x -1)/(2x^3 +1), is defined as the quotient of two polynomial functions. The initial inquiry about the validity of 5^x in a polynomial is addressed, confirming its invalidity. The conversation also touches on the nature of the responses, emphasizing the importance of clear communication. Overall, the consensus is that 5^x does not qualify as a polynomial term.
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y=(5x^4 + 5^x -1)/(2x^3 +1)

More specifically is 5^x a valid term in a polynomial?
 
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joshonator said:
More specifically is 5^x a valid term in a polynomial?

It is not.

A rational function is defined as the quotient of two polynomials functions. Like you said, 5x is not a valid term of a polynomial.
 
checkitagain said:
gb7nash,

there is no "like you said," because the OP didn't state that 5^x isn't
a valid term of a poynomial. He asked if it was.

...and gb7nash answered him. Is this really something to nitpick about?
 
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