Which expression is a polynomial in (x), if (a) and (b) are constants?

Correct answer: \(ax^3+bx+9\)

In option A, the powers of \(x\) are \(3\), \(1\), and \(0\). All are non-negative integers, so \(ax^3+bx+9\) is a polynomial in \(x\). Option B contains the negative exponent \(x^{-1}\). In option C, \(\frac{a}{x^2}=ax^{-2}\), which also has a negative exponent. Option D contains \(\sqrt{x}=x^{\tfrac{1}{2}}\), a fractional exponent. Exam tip: every exponent of the variable in a polynomial must be one of \(0,1,2,3,\ldots\).