In which expression are all powers integers, yet it is not a polynomial?

Correct answer: x⁻² + x³

Being an integer is not sufficient for an exponent to be permitted in a polynomial. Polynomial exponents must be non-negative integers. In option B, the powers −2 and 3 are both integers, but −2 is negative. Since x⁻² = 1/x², the expression contains the variable in a denominator and therefore is not a polynomial. Option A has powers 2, 1 and 0, all allowed. Option C has powers 4 and 0, also allowed. In option D, x⁰ = 1, so its effective powers are 0 and 1, both valid. Therefore option B is correct. This question distinguishes the broader set of integers, which includes negative numbers, from the narrower set of non-negative integer exponents required by the polynomial definition.