Question

Question content area top
Part 1
Determine whether the function is a polynomial function. If it​ is, identify the degree.
​h(x)equals5 x Superscript 5 Baseline plus 3 x cubed plus StartFraction 2 Over x EndFraction
Question content area bottom
Part 1
Choose the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
It is a polynomial. The degree of the polynomial is
  
enter your response here.
B.
It is not a polynomial.

Answer 1

To determine if the function \( h(x) = 5x^5 + 3x^3 + \frac{2}{x} \) is a polynomial, we need to remember that a polynomial function must have non-negative integer exponents for all terms.

Examining the terms in \( h(x) \):

1. \( 5x^5 \) - This term has a non-negative integer exponent (5).
2. \( 3x^3 \) - This term also has a non-negative integer exponent (3).
3. \( \frac{2}{x} \) - This term can be rewritten as \( 2x^{-1} \), which has a negative exponent (-1).

Since the last term has a negative exponent, the function \( h(x) \) is **not** a polynomial.

Therefore, the correct choice is:
B. It is not a polynomial.