Question

determine whether the function is a polynomial function. if it is, identify the degree.

(h(x) = 8x^5 + 4x^3 + \frac{4}{x})

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
b. it is not a polynomial.

Explanation:

Analyze the given function

Using the Polynomial Functions knowledge point

$$ h(x) = 8x^5 + 4x^3 + \frac{4}{x} = 8x^5 + 4x^3 + 4x^{-1} $$

Determine if it is a polynomial

Using the Polynomial Functions knowledge point
A polynomial function must have only non-negative integer exponents. The term \(4x^{-1}\) has a negative exponent \(-1\), so \(h(x)\) is not a polynomial function.

Select the correct option

Using the Polynomial Functions knowledge point
Option B states "It is not a polynomial", which is correct.

Answer:

• (A) It is a polynomial. The degree of the polynomial is [ ]
• (B) It is not a polynomial. (Correct answer)