PolynomialExpressionQ

PolynomialExpressionQ[expr, x] gives True if expr is structurally a polynomial expression in x, and False otherwise.

• PolynomialExpressionQ[expr, {x, y, ...}] gives True if expr is structurally a polynomial expression in x, y, ..., and False otherwise.
• PolynomialExpressionQ[expr, {x, y, ...}, test] gives True if expr is structurally a polynomial expression in x, y, ... with coefficients satisfying test.

Examples

Test if an expression is a polynomial in x:

PolynomialExpressionQ[x^2 + 3x + 1, x]
(* True *)

Non-polynomial expressions:

PolynomialExpressionQ[Sin[x] + x^2, x]
(* False *)

Test for integer coefficients:

PolynomialExpressionQ[2x^2 + 3x + 1, {x}, IntegerQ]
(* True *)

Please visit the official Wolfram Language Reference for more details.