Question

Determine whether the following function is a polynomial function. If the function is a polynomial function, state its degree, if it is not, tell why not. Write the polynomial in standard form. Then identify the leading term and the constant term.

f(x)= 4x + x⁴

Answer 1

The given function is a polynomial function of degree 4 in standard form.

Step-by-step explanation:

The given function is f(x) = 4x + x4. To determine whether this function is a polynomial function, we need to check if all its terms have non-negative integer exponents. In this case, the function is a polynomial because all its terms have exponents of 1 and 4, which are non-negative integers.

The degree of a polynomial is the highest exponent of the variable. Since the highest exponent in this function is 4, the degree of the polynomial is 4.

The polynomial in standard form would be f(x) = x4 + 4x.

The leading term is the term with the highest degree, which in this case is x4. The constant term is the term without any variable, which in this case is 0.