If xnx^nxn is a term of a polynomial, then the exponent nnn must be a non- negative integer. This means nnn can be 0, 1, 2, 3, and so on, but not negative or fractional. This restriction arises because polynomials are defined as algebraic expressions consisting of variables raised only to whole number powers (including zero), multiplied by coefficients, and combined using addition, subtraction, and multiplication. Any term with an exponent that is negative, fractional, or not an integer would disqualify the expression from being a polynomial
. To summarize:
- nnn is a whole number (integer)
- n≥0n\geq 0n≥0 (non-negative)
Thus, nnn is a non-negative integer in the context of polynomial terms
