Which expression is a polynomial in (z)?

Correct answer: \(3z^4-z^2+8\)

In \(3z^4-z^2+8\), the powers of \(z\) are \(4\), \(2\), and \(0\), all of which are non-negative integers. Therefore, it is a polynomial in \(z\). In \(z^{-1}+2\) and \(\frac{6}{z}+1\), \(z\) has a negative power, while \(\sqrt{z}+5\) contains \(z^{\frac12}\); hence, these are not polynomials. Exam tip: powers of the variable in a polynomial must be \(0,1,2,\ldots\).