A polynomial uses whole-number powers of the variable and no variable in a denominator or root. Constants also count as polynomials. A polynomial can include constants and non-negative whole-number powers of x. Expressions with x in a denominator or under a root are not polynomials. The correct choices are 9, x³ − x, 5x − 7, x² + 3x + 1, because each of these satisfies the required condition.