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) = 2x + x^4\\)

Explanation:

Analyze the function type

$$ f(x) = 2x + x^4 $$

The exponents of the variable \(x\) are \(1\) and \(4\), which are non-negative integers. Thus, \(f(x)\) is a polynomial function.

Determine standard form and degree

$$ f(x) = x^4 + 2x $$

The highest exponent is \(4\), so the degree is \(4\).

Identify leading and constant terms

The term with the highest power is \(x^4\), so the leading term is \(x^4\).
There is no explicit constant term, so the constant term is \(0\).

Answer:

• Is the function a polynomial? Yes.
• Degree: \(4\)
• Standard form: \(f(x) = x^4 + 2x\)
• Leading term: \(x^4\)
• Constant term: \(0\)