Which statement is correct for \(\frac{x^4}{3}-\sqrt{10}x^2+7\)?

Correct answer: It is a polynomial of degree \(4\)

The expression is \(\frac{1}{3}x^4-\sqrt{10}x^2+7\). In a polynomial, the powers of the variable must be non-negative integers. Its coefficients may be fractional or irrational real numbers. The highest power of \(x\) is \(4\), so it is a polynomial of degree \(4\). Both \(\frac{1}{3}\) and \(-\sqrt{10}\) are coefficients, so options A and D are incorrect. Exam tip: find the degree from the highest exponent of the variable, not from the type of coefficient.