Question

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

(f(x) = 3x^5 + 6x^7)

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 definition of a polynomial function

A polynomial function is a function consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
The given function is:

$$f(x) = 3x^5 + 6x^7$$

Both exponents, \(5\) and \(7\), are non-negative integers. Therefore, \(f(x)\) is a polynomial function.

Determine the degree of the polynomial

The degree of a polynomial function is the highest power of the variable \(x\) in its terms when written in standard form.
In the expression \(3x^5 + 6x^7\), the terms have exponents \(5\) and \(7\).
The largest exponent is \(7\).
Thus, the degree of the polynomial is \(7\).

Match with the given choices

Since the function is a polynomial of degree \(7\), we select option A and fill in the blank with \(7\).

Answer:

• (A) It is a polynomial. The degree of the polynomial is 7 (Correct answer)
• (B) It is not a polynomial.