Which of the following expressions is an example of a polynomial in one variable?

Correct answer: \(5x^3-2x+7\)

In \(5x^3-2x+7\), the powers of \(x\) are \(3\), \(1\), and \(0\). All are non-negative integers, so it is a polynomial in one variable. In option B, \(\frac{3}{x}=3x^{-1}\), and option D also has a negative exponent; option C has \(\sqrt{x}=x^{1/2}\), a fractional exponent. Exam tip: every exponent of the variable in a polynomial must be a non-negative integer.