Question

which of the following expressions are polynomials and which are not? why?
\\(\frac{1}{x^3} + x^2\\)
answer
the expression is .

Explanation:

A polynomial is an expression consisting of variables and coefficients, constructed using only addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Rewrite the first term: $\frac{1}{x^3} = x^{-3}$. This term has a negative exponent, which violates the polynomial definition.

Answer:

not a polynomial, because it contains a term with a negative exponent ($x^{-3}$) and polynomials can only have non-negative integer exponents on variables.