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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.
An equation has an equal = sign whereas an expression does not.
algebric uses variables and numerical uses numbers
An algebraic function is a function built from polynomial and combined with +,*,-,/ signs. The transcendental it is not built from polynomial like X the power of Pie plus 1. this function is transcendental because the power pi is not integer number in result it can't be a polynomial.
Numerical expressions solely include numbers, while algebraic expressions may contain a variable like x. An example of a numerical expression is 1+2 and an example of an algebraic expression is 2x+3y=0.