Why is (x^2+3x^{1/3}+4) not a polynomial?

Correct answer: Because the exponent of the variable in \(x^{1/3}\) is not a non-negative integer

In a polynomial, every exponent of the variable must be a non-negative integer such as \(0,1,2,\ldots\). Here, the exponent of \(x\) in \(x^{1/3}\) is \(1/3\), which is not an integer, so the expression is not a polynomial. The term \(x^2\) and the constant \(4\) are valid in a polynomial, and the number of terms does not matter. Exam tip: first check the exponents of variables when identifying a polynomial.