Q: What are the conditions that an algebraic expression is not a polynomial?

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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.

Related questions

A polynomial is always going to be an algebraic expression, but an algebraic expression doesn't always have to be a polynomial. In another polynomial is a subset of algebraic expression.

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.

A polynomial is a type of algebraic expression. They differ in the number of terms that contain variables. An algebraic expression has at least 1 variable, while a polynomial has multiple terms with variables in it.

Yes.

Yes

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).

An expression is non polynomial if it has : negative exponent fractional exponent variable exponent in the radicand

Yes

It is an algebraic factor.

monomial binomial trinomial polynomial

No. A matrix polynomial is an algebraic expression in which the variable is a matrix. A polynomial matrix is a matrix in which each element is a polynomial.