Which statement is correct for \(\frac{x^3}{4}-\sqrt{6}x+10\)?

Correct answer: It is a polynomial of degree \(3\)

In \(\frac{x^3}{4}-\sqrt{6}x+10\), the powers of \(x\) are \(3\), \(1\), and \(0\), all of which are non-negative integers. Therefore, it is a polynomial. Polynomial coefficients may be real numbers, so both \(\frac14\) and \(-\sqrt{6}\) are valid coefficients. The highest power of \(x\) is \(3\), so its degree is \(3\). An irrational coefficient such as \(\sqrt{6}\) does not make an expression non-polynomial. Exam tip: find the degree by identifying the greatest exponent of the variable, not by checking the type of coefficient.