For which (n) will (4x^n+3x^2-1) not be a polynomial?

Correct answer: \(n=-2\)

In a polynomial, the exponents of the variable must be non-negative integers. For \(n=-2\), the expression contains \(4x^{-2}=\frac{4}{x^2}\), so the variable occurs in the denominator; hence it is not a polynomial. In contrast, when \(n=0\), \(4x^0=4\) is a constant term, so the expression remains a polynomial. Exam tip: a negative or fractional exponent means the expression is not a polynomial.