When it has any term in which the variable is not raised to a non-nagative integer power.
So for example, if it contains a term such as x-3 [the power is not positive]
or x1/2 or sqrt(x) [the power is not an integer]
or sin(x), or log(x) etc [not powers of x].
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A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. An algebraic expression is an expression with a variable in it, and a polynomial is an expression with multiple terms with variables in it.
if it has parentheses
Not really.For example: x can be considered and algebraic expression by itself, however it is only a single variable, so by definition it is not a polynomial expression (multiple-number expression).
monomial binomial trinomial polynomial
A polynomial is one possible answer.