They are terms in which a variable is raised to the same power (index) in both terms.
So x2y and -27x2y are like terms but not xy2.
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As many as you like. The highest power of the variable in question (usually x) defines the degree of the polynomial. If the degree is n, the polynomial can have n+1 terms. (If there are more then the polynomial can be reduced.) But there is NO LIMIT to the value of n.
A polynomial with three terms is called a trinomial. Example: x² + 16 + 18 is a trinomial. It has three terms (x²), (16), and (18)
A trinomial
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.
Two terms is a binomial. More than two terms is a polynomial. Binomials are not part of the set of polynomials.